Conceptually, EAW runs a different idea of the relation of armies to corps. Once you understand this, it is an excellent simulation of the WWI era armies.
To get 'any' benefit, corps need to be in the same or an adjacent region as an army. Corps do not embed inside the army (although they can). Instead they stack in the same region or an adjacent region.
An army force can support any adjacent corps with March to the Sound of Guns just like in all other AGEOD games. But corps are not subordinate to an army as in CW2. Instead, any army in the same or an adjacent region can attach that corps for battle. Think of armies as units which can use and corps in the region or an adjacent region OR which will support any corps in the same or any adjacent region.
You can use the coordinated march as in other AGEOD games. The limit is the same, if the army and corps all have selected the coordinate movement command and start in the same region, they will move together.
Army group is not really a concept useful to understanding this game. Instead, each side has a supreme command which must be in command range of three star generals in order for the general to be promoted to army command.