Given a finite group $G= H \ltimes N$ (with no particular constraints on $H, N$), it's probably been known for a long time how to describe efficiently the possible subgroups of $G$. A graduate student was asking me about this, having dug a version out of an obscure research paper in the process of studying an unrelated technical problem. I'm not sure what exists in group theory books or other such sources. The answer seems to have the flavor of cocycles and coboundaries but is apparently somewhat complicated to write down.
Is there a convenient reference giving a recipe for all subgroups of a finite group written as a semidirect product of two known groups relative to a known action of one on the other?
Best Answer
Usenko, Subgroups of semidirect products, Ukrainian Mathematical Journal, 1991, Volume 43, Numbers 7-8, Pages 982-988