Let Sn be the group of permutations on n symbols Then 1. S4 has no subgroup isomorphic to S3 2. S4 has only one subgroup isomorphic to S3 3. S4 has exactly 3 distinct subgroups isomorphic to S3?
It has 4 subgroups isomorphic to S3. If you hold each of the 4 elements fixed and permute the remaining three, you get each of the 4 subgroups isomorphic to S3.
