I did some digging. Each branch of sevice is different but the Army usually has six four star generals. One is the Army Chief of Staff who is also one of the Joint Chiefs. The Vice Chief of Staff is also a four star. The commanders of US Army Europe, the Training and Doctrine Command (TRADOC), FORSCOM (US Army Forces Command) and the US Army Materiel Command. The latter is what General Anne Dunwoody was nominated for.
To break down the other general ranks a bit.
Lieutenant General (three stars)- These are normally Corps commanders or officers that have command over a very large number of soldiers (anywhere between 20,000-45,000). I was part of VII Corps during Desert Storm, which was larger than an average Army Corps. The primary divisions of the Corps were the 1st Infantry Division (my division), 1st Armored Division and the 3rd Armored Division, along with the 2d Cavalry Regiment, 1st Cavalry Division, 11th Aviation Group and the British 1st Armoured Division.
Major Generals (two star) are normally division commanders.
Brigadier Generals (one star). They have a number of roles, one of which is as assistant division commanders.
There is a ceiling to the amount of general officers that the army can have, I think it's close to 300.
Officers are all well and good but it's the NCO's that are the backbone of the Army.