Army and marine corps are slightly diff, but as i know it , in the Marines our basic infantry makeup is like this:
FireTeam - FireTeam Leader, Machine Gunner, Assistant Gunner and "Ready" aka pointman. (short version is "Ready,Team,Fire,Assist" in that order because thats the typical line up in a tactical movement formation)
Squad - 3 sometimes 4 fireteams
Platoon - 3 squads
Company - 3 platoons
Battalion - usually 3 Companys, with an extra company called the HQ Company some battalions also have a Weapons company for mortars, rockets and heavier machine guns.  you can also add in combat engineer/bridging companies or other special ability companies.
Regiment - ~3 Battalions
Division not sure how many regiments to a Division, but basic rule of thumb is 3 units to the next level of command.
Corps - 3 Divisions (US Marines have a 4th Division which is the includes all the Reserve units)
The Marine Corps are basically one 'Corps' hence the name, go figure, the Army has many corps, because they are much larger. and also brigades, but im not sure where brigades fit in.  But there aro so many special units and divisions (bootcamp, specialist training, special forces, etc that the typical structure is broken quite often, but in a combat situation its pretty typical that everything is broken down by the rule of 3's, every unit has 3 subordinate units to worry about, which keeps the organization management from being "flattened" (if one manager has to worry about 12 people reporting to him, things will get missed) so to speak, which makes decision making slower in a lot of cases.