[GAP Forum] extensions of subgroups of a finite 2-group

[Petr Savicky]

Dear GAP Forum:

Assume, G is a finite 2-group and A is its subgroup.
The groups may be permutation groups or pc groups.
I would like to construct all extensions B of A, such
that [B:A] = 2.

One way is to perform

    N := Normalizer(G, A);
    R := RightTransversal(N, A);
    L := [];
    for elm in R do
        if elm in A then
            continue;
        fi;
        if elm^2 in A then
            Add(L, ClosureGroup(A, elm));
        fi;
    od;

Is there a better way?

Another question is as follows. Let G be a 2-group
and H and A its subgroups, such that the intersection
of H and A is trivial. Is it possible to determine
in GAP, whether there is a subgroup B of G, such
that B contains A and is a complement of H in G?

I appreciate any help concerning these questions.

Best regards,
Petr Savicky.