Finding sup[er]groups of a group
Is there any implemented algorithm [or any algortihm which is not too slow or hard to implement] to find the supgroups of a given group? More precisely, say I have a permutation group H which is given as a subgroup of Sn (the permutation group on n elements) and some integer k. Is there a way to find supgroups K of H so that the index of H in K is equal to (or is at most) some number k?
Just extend the set of generators with more and more elements to get larger groups.