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Without organization, you are doomed
You can build a tank division to have high organization but really you're wasting slots. And really the bottom line too is that you either have the tank doctrine or you have something else.
The only way you get a tank division to have high ORG (and still be amazing) is when you start making space marine templates.
Half tanks and half infantry is a good starting point. You can tweak it from there based on your specific situation such as available equipment, templates, and org bonuses. I am usually comfortable with org being around 40 or better. Try not to let it dip much below that if you can help it.
Tanks by default have lower organization than all other units, bt that is because they bring the potential for an armor advantage. If a tank divisions Armor is not pierced by a division that is fighting it, the tank division doubles its number of attacks AND increases the size of dice rolled for that damage; enemies that can't pierce the tank also do half damage to the tank division. In effect, if your tank division has at least half the organization of the units it will fight, then it has enough organization, because it is twice as good. Usually, this number will float around 30-35.
Cavalry with basic infantry is both an expensive template to create in the division designer, and elimantes the advantages held by both unit types. Cavalry have extra movement speed, which is lost if paired with infantry. Although cavalry start with higher organization, there are almost no doctrines that benefit cavalry, making them inferior to infantry in every category except speed (and including organization) after the first few in-game years. There is almost no reason to every mix "mobile" and "infantry" unit types in the same division, though there are some for "tank" with "infantry", and "tank" with "mobile".
Here's the difference:
Each round of combat deals HP and Org damage, and when a unit's HP reaches 0 it is destroyed and when Org reaches 0 it is forced to retreat. The latter is to simulate a unit being suppressed, outmaneuvered, unable to handle growing battlefield chaos, breakdowns in command & control, facing too much pressure etc, and being unable to continue fighting. Units running out of Org are not destroyed so much as they become combat-ineffective and are forced to retreat and rest up.
Here's why Org is more important:
While HP (or "strength") may seem more intuitive, it is actually not all that important: units are more or less never destroyed in battle unless they have single digit strength levels, and outside of that specific scenario units will always run out of Org before HP.
With regards to tanks:
Tanks have super-low HP, and from your post it seems they have low Org too, however this does not matter because tanks have Armor, Breakthrough, and Hardness to make up for that.
Hardness determines how many Soft and Hard attacks a unit takes. Having high Hardness in and of itself is protection considering most divisions will have far lower Hard Attack than Soft Attack.
Breakthrough is the ability of a division to prevent damage on the attack, and tank battalions are a large source of Breakthrough. An infantry division may only have a Breakthrouhg value of, say, 60, wheras a tank division may have a breakthrough level of anywhere from 200-500+. In addition, it's worth noting that tanks have very low Defense values (the ability of a unit to avoid damage while defending), about 1/4th of an infantry battalion. They are still good in other important stats that help them avoid damage, but holding the line is for infantry divisions, not tank divisions.
Armor is the counter-stat to Piercing, and it's very important for determining whether or not a given division has a very powerful combat bonus. Essentially, if a division's Armor is higher than an enemy division's Piercing, then the division takes 50% less HP and Org damage and also deals out 50% more Org damage. Having higher Piercing than enemy Armor doesn't given you a bonus but at least denies the enemy the Armor bonus.
The way Armor and Piercing is calculated is a weighted average: for Armor, it is 30% of the highest-Armor battalion plus 70% of division average, wheras Piercing is 40% of highest value and 60% of the average. This is why, for example, adding a single AT battalion might increase Piercing by 50 but a subsequent battaltion might only increase it by 10.
All in all, tanks provide serious offensive capabilities to a division. Unless you are role-playing UK's horrible infantry tank doctrine which spread out their most powerful tanks amongst their infantry units it is best advised you concentrate tanks into a handful of very powerful divisions. 5-10 divisions may not sound like much, but with 3 powerful defensive statistics they can be incredible; take care of them and they will take care of you.
More Notes on Armor and Piercing:
Whether or not you have this bonus and whether you piercing denies the enemy this bonus is indicated in each division box in the battle screen. A golden shield means none of the enmy divisions can pierce it's armor, a cracked grey shield means at least 1 enemy divsion can pierce it, and an arrow means it can pierce enemy divisions.
Note that divisions on both sides of a battle may have the armor bonus.
Hover over division boxes in the battle screen to see the enemy divisions' Piercing and Armor values so you can adjust your own division templates to counter them.
The basic idea behind AT vs. Armor development is this: AT guns will be able to pierce Medium tanks of the same generation (i.e Improved AT vs Medium Tank 2) but not heavy tanks. Medium tank destroyers can destroy obsolete heavy tanks (i.e. Medium Tank Destroyer 3 vs. Heavy Tank 2) but only modern heavy tank destroyers can pierce heavy tanks. Infantry AT weapons are really only good for piercing mechanized transports and light tanks and for not dragging down the division Piercing average too much.
In fast offensive divisions org is not so important. You usually have superiority and can deploy reserves. You do need enough to win a bit. If you have motorised divisions to hold the territory you capture then it doesn't matter much if the tanks have low org when they move forward.
Also note that the rate org is lost and recovered from combat or moving is independent of the amount of org. If you are using Mobile Warfare then, depending where you are in it, tanks may have a higher recovery rate than infantry (if you went right-side). That means a tank heavy division will be able to sustain combat better than one with more infantry.
unless the enemy breakthrough you will stand until org is lost. (or strength but less likely)
in defense if org is low you will not be able to hold as unit retreats before reinforcements arrive. In offensive, you will lose org moving, if you lose too much, then you retreat quickly if attacked in the new sector. This is very important in poor terrain such as Russia and Africa.
I would argue that arty produces a lot of damage to unit strengths but has low org by itself.
Tanks give hardness, breakthrough, but are vulnerable to low org and supply shortages.
best used to pierce and blitz through, but need to withdraw and rest to regain supply and org.
Tank fighting should never be done without supporting infantry (irl). Inf do a lot of the fighting and get killed / exhausted fast. (hence need for lots)
During ww2 units were reorganised often to add infantry (motorised or mech).
During operation market garden (a bridge too far). The tanks had to stop because they outran inf support.
Do not add inf to tanks unless it is a slow breakthrough unit. you lose the speed.
high tank % reduces damage (due to hardness) but has low org, so the mot / mech add org,
allowing it to last long enough to do its job.
tank + cav early attack unit +speed + cav def when short of fuel - slow speed - vulnerable. Uses points that may be best used elsewhere.
inf hold but best with engineer (entrench) arty (damage attacker) - slow
inf + tank hold with less losses, may be a waste of tank - add eng and arty
tank only - very low org, will prob run out of org and lose.
tank + mot - fast but requires fuel.
tank + mech - fast (not first level mech) requires lots fuel, reduced losses, expensive
I add one or two art if possible line or support esp to attack divs. 1 to defence.
eng for attack speed, entrenchment in defence -other benefit at higher level
logistic - lower fuel
maint - lowers equip loss - good for attack divs.
recon - tactics choice and I think move speed.
mp - only in garrison units.
aa - can add soft attack - less important if you have air support.
The more armour the less losses so can replace arty with SParty etc.
some doctrines (blitzkrieg) can add org to armour divs thus make it viable to run more armour less inf in templates.
Many commenters here overestimate the usefulness of organization. In essence organization is equivalent to morale, it represents how long a division can fight before being forced to retreat. When your division has low organization, it can be forced to either retreat or cancel their attack before a positive outcome has reached. This makes organization an important statistic. Organization however does not make a bad unit template better. If you push a frontline with infantry divisions without enough breakthrough or a lot of soft attack, more organization won't make you win more, but it will make you lose slower.
A good example would be comparing organization to hitpoints in other games. Having 200 hitpoints if better than having 100. If your opponent however outclasses you by a large margin in damage dealt/DPS, they might still win despite your higher hitpoint pool. Depending on the division type, having 30-40 organization is usually more than enough.
IRL this is exactly what happens with FL units, they fight for a spell then rotate out to reorganise and replenish.
Not sure if that helps the OP but it certainly helped this player get his head around the concept.