It is well known that a virtually cyclic group is either finite, or finite-by-(infinite cyclic) or finite-by-(infinite dihedral).
I want to know if there is some similar description for f.g. virtually abelian groups, or even for simpler groups (e.g. virtually (free abelian of rank 2)). In the affirmative case, are the proofs easy/short? References are welcome too.
Thank you!