: We know the soldier Orcs had identification numbers. And we know there were hordes of slaves in Mordor, some human, some Orcish, which performed non-military tasks, such as raising food, caring for the roads, etc.

: Minas Morgul was "ruled" by the Lord of the Nazgul, and Dol Guldur was "ruled" by Khamul the Easterling. These were both on a par with "colonies" or "satellite states", I think, even though Dol Guldur was technically more ancient than Mordor (in the Third Age).

: The Mouth of Sauron was the Lieutenant of Barad-dur, and Gothmog was the Lieutenant of Minas Morgul. I suspect these were "ranks", not in the sense of "lieutenant answers to captain", etc., but rather, in the sense that they indicated special positions of importance within the hierarchy.

: So, I'm curious, how would the rest of you devise a structure for representing Mordor's government and military?

First of all, Sauron, the Head Man, the Big Cheese, the High Muckamuck.

Then, the Lord of the Nazgul (Er-Murazor to MERPS folks), Sauron's second in command, the VP, the Second Banana.

Then Khamul (the Black Easterling, the Dragon Lord, etc.) as warden of Dol Guldur and second-most experienced Ringwraith.

Then Gothmog and the Mouth as the wardens of their towers.

Then the other seven Ringwraiths.

Then any ambassadors.

Then human generals.

Then Uruk-hai generals.

Then Olog-hai troops.

Then other Troll troops.

Then Human troops.

Then Uruk-hai troops.

Then Snaga troops.

Then Human slaves.

Finally Snaga slaves.