I did not actually work out the details for this problem, but I had an idea that you might want to try. Let i.e. all permutations that fix 4. Then it is seem that (in fact is naturally isomorphic to ). Now since is not normal it means .Ifi.e. if there is so that then it means ispropelycontained in . By Lagrange's theorem it would mean since . But . Therefore, . I cannot gaurentte you this would work because I was kinda lazy to work out the details but this would be the first thing I would try to do.