Platoons, Brigades, Divisions Oh My!
Here is a general descriptor of how the army is structured. Don't get too caught in the numbers though. Sections will vary in size. Platoons may be short sections (or may have extra sections). Regular Force infantry battalions only have three rifle companies these days (as opposed to the traditional four) and many reserve regiments only have one company.
Note that generally the "rule of three" gives you a rough estimate of what an element can be broken down in to (ie: 3 sections to a platoon, 3 platoons to a company, 3 companies to a battalion, etc, etc). However, that rule of three typically breaks down when you try to apply it to support elements or combined arms groups.
. - Detachment, Crew or fireteam
.. - Section
A section normally numbers about 8-10 men and is commanded by a Sgt with a MCpl as second in command.
... - Platoon or Troop
A platoon is a basic building block unit of organization. They are headed by a junior officer (2Lt to Capt) and number about 30 to 45 members. They consist of 3 or 4 sections (depending on the Arm). A Tank Troop would consist of 4 battle tanks.
l - Company
ll - Batallion
lll - Regiment
(Common for Soviet units and WWII German ones, in which a Regiment was a fighting formation)
x - Brigade
(The term Brigade Group is often used to designate a combined arms Brigade)