Avital Oliver asked the following question:
I accidently found a function SubdirectProducts which isn't documented. Can
I count on this function to work and return all the subdirect products of
The function SubdirectProducts( S, T ) computes all subdirect products
of S and T up to conjugacy in the direct product Parent(S) x Parent(T).
The subdirect products are returned as subgroups of the direct product
Parent(S) x Parent(T).
Hence, if you set up your groups such that Parent(S) = S and Parent(T) = T,
then you will get all subdirect products up to conjugacy in S x T.
If you have groups S and G and you want G to be the parent of S, then you
can achieve this by 'S := Subgroup( G, GeneratorsOfGroup(S) );' (Provided
that S is indeed a subgroup of G of course.)
Best wishes, Bettina