A simple reply goes something like this:
A Battalion consists of 3 (triangular) or 4 (square) (or 5 or 6) companies. You see, each nation at different points in time might construct a battalion in different manner. At any one point in time a nation may construct battalions of Armour, Infantry, Artillery, Marine or Airborne infantry in totally different manner.
A Brigade folows the same rule; typically a Brigade will consist of 3 primary battalions plus several companies of other arms in support. Such supporting arms might include anti-aircraft, or anti-tank defense, plus some engineer or heavy weapons support. In some nations, a brigade is similar to a regiment; see below.....(but do not assume that the two words are interchangeable).
A division is again, something quite flexible in concept. A division might contain 3 primary brigades or regiments plus supporting regiments (brigades) plus supporting service, signal, medical, transport, engineer or reconnaissance battalions. And to add to the confusion, any nation might have any number of permutations of size according to period, application theatre, etc.
Add to this the reality that many nations were never able to fill their divisional formations with a correct (paper) number of men or equipment and you are no more the wiser.
To make things simpler, think in threes, since most nations abandoned the square formation at one point or another.
3 Companies of infantry form a infantry battalion
3 battalions form a regiment and 3 regiments will form a division.
At each level add on extra resources; divisions get supporting regiments and battalions, regiments get supporting battalions and companies, etc
Ask about a particular division at a particular time and can you expect a clear and concise answer?
Probably not.
Paper strengths almost never approached reality and operational considerations over-rode any theoretical numbers.
You didn't ask about Corps?
