Many thanks to all who answered my questions!
The groups I am interested in are not very big, at most some hundred
elements, but can be rather complicated in structure.
My first problem is to recognize some groups from the literature or other
computations in the complete lists of (small) solvable groups (or
p-groups) contained in GAP, so that I get a complete overview of
the possibilities. Some of the groups are given by relations, some
as permutation groups and some as semidirect products or otherwise.
The second problem is to recognize subgoups and/or factor groups of
(solvable) groups in the given lists or to test isomorphism with
other subgroups/factor groups. Especially the isomorphism test
between subgroups should happen automatically (the groups involved
in this are very small!)
A further problem I am faced with is the computation of the
ConjugacyClassesSubgroups(G). I didn't try this with GAP 3.2 yet,
but for some groups of order 256 it took several hours with 3.1.
Did these routines improve? What I am really interested in are
the normal subgroups of G; is there a simpler way to compute them?
(Abelian groups and groups of nilpotency class 2 can be excluded.)
I intended to wait with further postings until I had taken a closer look
at GAP 3.2. But as some people showed their interest in these problems
I am now taking the easy way and ask the specialists for their