@barnee
Hi barnee,
An Army Group must organized from the start of the players turn - in other words: it must be formed on a previous turn - to be active.
The Armies within an Army Group can stil re-form during Non-Combat Movement - as with the standard rules for Panzer Armies, Tank Armies, Waffen-SS Armies and Soviet Army Corps.
The Army Group Marker is not a unit that can be chosen as casualty - it only represents an organizational symbol.
Remember:
When an Army Group suffers casualtiues during combat, the Army Group Marker is removed as soon as the Army Group no longer contains 2 complete Armies and at least 10 other land combat units.
In this case the Army Group no longer exists as a fighting force - and all units and Armies (if any) are reduced to fight on their original combat terms.