The unit “division” is separate from a brigade. While the Imperial class star destroyer (Imperator class at the time of the Clone Wars) is typically stated to carry one division plus support personnel, indicating a division in the later Imperial era is the same size as an un-augmented brigade, these statements clash with other statements made that indicate that the unit it carries is actually a brigade. In military terminology a division is larger then a brigade. Further, we know the unit known as a “division” was common in the old Republic (The Imperial Sourcebook), yet General Jurokk identified the unit following Lord Vader into the Jedi Temple as a “brigade” when Order 66 was executed, showing that brigade is a separate unit. (Revenge of the Sith novel) Whether or not the unit “Grand Army” is appropriate is questionable as well. The term “Grand Army of the Republic” is typically used encompassing the Army, Marines, Navy, and Starfighter Corps, not just the army. This makes it unlikely that the unit “Grand Army” is the sum total of all the Republic clone troopers. More likely is that a “Grand Army” is just another, larger unit similar to the later Oversector Commands (Before the Storm; Star Wars RolePlaying Game second edition). These then would the larger, mobile commands ranking Jedi could assemble that the Guide to the Grand Army of the Republic describes. They would represent ten sector armies in normal form, it is unknown if the expanded version would be twenty expanded sector armies, or just ten. The total number of Grand Armies is also unknown. System armies protect individual systems, with sector armies defending the sector capital and responding to crises in the sector (e.g. invasion or secession of a local planet). Any larger unit could call upon smaller units to reinforce them. (The Imperial Sourcebook)
Grand Army of the Republic
Squad – 9 clone troopers
Platoon – 4 squads normal (36), 8 squads expanded (72)
Company – 4 platoons normal (144), 8 platoons expanded (576)
Battalion – 4 companies normal (576), 8 companies expanded (4,608)
Regiment – 4 battalions normal (2,304), 8 battalions expanded (36,864)
Brigade – 4 regiments normal (9,216), 8 regiments expanded (294,912)
Division – 2 brigades normal (18,432), 4 brigades expanded (1,178,648)
Corps – 4 brigades normal (36,864), 8 brigades expanded (4,718,592)
Army – 4 corps normal (147,456), 8 corps expanded (37,748,736)
System Army - 2 armies normal (294,912), 4 armies expanded (150,994,944)
Sector Army – 2 system armies normal (589,824), 4 system armies expanded (603,979,776)
Grand Army – 10 sector armies normal (5,898,240), 10 (?) sector armies expanded (6,039,797,760)
The troop listings do not include in them officers, senior NCOs, headquarters elements, support personnel, or droids. However, extrapolating out this to the known territory of the Republic and using the above figures results in a total of 353 billion clone troopers for the member systems alone (181 trillion using expanded figures), with another 3.5 billion for the total sector armies from the derived minimum of 6,002 sectors (3.6 trillion using expanded figures). Including the smaller systems as well and assuming 6,002 sectors results in a total of 70.8 trillion clone troops (36 quadrillion using expanded figures).
However, this organization of forces does not match what we see in the films. In Attack of the Clones General Windu is given command of five units. As he leaves to engage the enemy, six clones follow him, and he joins another group of six clones and some other Jedi. As neither six nor twelve is evenly divisible by five, it appears that a “unit” in the Grand Army of the Republic numbers six clones and an NCO/Officer. This appears to be confirmed in Revenge of the Sith, as organizations divisible to 6 men or 6 men and an NCO/Officer are common – It is seen with Commander Appo on the Jedi Temple hangar entrance; 6 men and their commander kill Generals Mundi and Secura, Commander Cody is seen backed by either 6 or 12 men.
This further follows with larger organizations. When Lord Vader marches on the Jedi Temple to complete Order 66 the units that follow him are in rows of 7 and columns of 12 for a total of 84. This would equate to 12 squads. If a platoon were 28 men, it would also follow there, for 3 platoons in each unit. However, platoons of 30 work better with the “Parade Ground” scene at the end of Attack of the Clones as well. There clones are seen in groups of 156 which then form up into blocks of 624. Five platoons and a command staff of 6 would equate to a unit of 156 men, which then joins with 3 other units to form one of 624, whose command staff is standing outside the formation. Republic Commando: Triple Zero states that the parade ground was showcasing “battalions”, providing a name for this larger unit. We see a group of 17 walk in front of a formation; if this was the command staff and their escort walking them to their battalion then each battalion would be 640 men strong. Thus if there were 4 battalions to a regiment and 6 regiments to a brigade the total would be just shy of the stated 16,000 capacity of an Acclamator. (Attack of the Clones Incredible Cross Sections)
The unit of 84 is an unusual outlier – perhaps 84 makes up the unit referred to as a Legion? If so it would certainly help explain how the Ewoks were able to overcome the Imperial Marines at Endor. That primitives could defeat 84 men is a far more plausible explanation then that thousands of men simply chose not to fight. Alternatively, the total size of the unit may not be visible. Six units of 84 are seen following Lord Vader, but it is probable that many more are out of view of the camera. If this were the case it would help match with the evidence - if a regiment has a command staff of 32, and a brigade one of 72, then not only would this fit with the known capacity of an Acclamator, it would also match the March on the Temple, as 186 formations of 84 would add up to a brigade – the unit identified by General Jurokk (Revenge of the Sith novel).