Actually, there were multiple Army Groups post-Normandy invasion ... the command rank to unit heirarchy breaks down at those levels of command, so you can't simply equate x-stars to y-command level.
Today, both Corps and Army-level commands are typically 3-star commands, and though they are different organizations there is some interchangeability, as depending on the type of Joint operation that is ongoing either a Corps or an Army can serve as the Land Component Command. In the CENTCOM (Theater-level command, 4-star) AOR today, 3rd US Army (Patton's Own) is the Land Component Command & Army Forces headquarters (Formally Coalition Forces Land Component Command, CFLCC, aka ARCENT dual-hatted), commanded by a 3-star, while the major operational command is a Corps headquarters (Formally Multi-National Corps Iraq, MNC-I, which is I think III Corps today, though I haven't kept up with the precise rotation schedule) also commanded by a 3-star.
Under the modular army, a division or brigade can be under the direct operational control of a Corps or Army without intervening headquarters, again depending on the operation, so the strict heirarchy of command that existed during WWI and similar conflicts doesn't actually continue quite the same today.
In other trivia:
In the artillery, a
battery is the name for a unit the same size/function as a
troop (cavalry) or
company (every other branch).
In the Army, cavalry operates in squadrons and aviation in battalions, while the USAF/USN/USMC use the term squadron for aircarft.
Cavalry operated in Groups and Brigades prior to the Korean War, where the Brigade/Group might be either a combination of cavalry regiments, or a reinforced cavalry organization. Post-Korea those formations standardized on troop/squadron/regiment nomenclature ... mostly. There is an exception -- 1st Calavry Division. One of two Cavalry Divisions at the start of WWII, 1st Cav was dismounted to fight as infantry in the Pacific. It was an infantry formation, later an airborne (one brigade) and airmobile formation during Vietnam. Its infantry battalions retained Battalion nomenclature (1st Battalion 8th Cavalry (Airborne)) rather than squadron nomenclature, except for the divisional cavalry squadron (1st Squadron, 9th Cavalry). Post-Vietnam 1CD became an armored formation, and for a time was an experimental triple-capability division of infantry-armor-airmobile formations. It retained its cavalry heritage but with armor/infantry battalions as an armored division through the 90s until modularized. It now has four Heavy Brigade Combat Teams and no divisional cavalry squadron (though each HBCT has a reconnaissance, surveillance, and target acquisition squadron that is essentially a form of cavalry outfit with a Cavalry designation, along with two combined arms battalions).
- And then there's the whole discussion about what dashes versus slashes mean in unit designations ...
... So depending on what historical era you pick, all sorts of naming conventions could be accurate.

The US Army has a whole organization dedicated to trying to keep the names and heritage straight (not to mention the unit crests and colors).
- Olgar (who has been a First Team -- 1st Cav -- soldier among other places)