- Thread starter
- Banned
- #1

G be a group with normal subgroups H1 and H2 with H2 not a subset of H1. Let K = H1 intersect H2.

Show that if G/H1 is simple, then G/H1 is isomorphic to H2/K.

My first thought was to set up a homomorphism with K as the kernel but soon realised that the fact that H2 was not normal is H1 scuppered this tactic. G/H1 being simple implies that H1 is the largest proper normal subgroup but where to go from there?