On the isomorphism between two finite groups

Question

Let $G$ be a finite group and $K,H$ be two normal subgroups of $G$ such that $N \cong K$. Then can we say that $G/N \cong G/K$?

you should at least try something before dumping questions on us. Questions such as this one are likely to be closed. — Ittay Weiss, Sep 24 '16 at 08:26

score 3 · Answer 1 · answered Sep 24 '16 at 08:22

3

With $G = Z_4 \times Z_2$, consider subgroups of order two.

answered Sep 24 '16 at 08:22

Bolton Bailey

@Hana: Check for yourself. – tomasz Sep 24 '16 at 08:24
Bolton, please avoid posting a comment as an answer. – Ittay Weiss Sep 24 '16 at 08:27
2

@Ittay, it's not a comment, it's a hint. – Gerry Myerson Sep 24 '16 at 08:59

1 Answers1