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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 $S_n$ (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 $k$?