Counterexamples to particular questions in group theory

Question

Let $G$ be a finite group with normal subgroups $N_{1}$ and $N_{2}$. Find counter examples to the following statements

1) If $N_{1}\cong N_{2}$ then $G/N_{1}\cong G/N_{2}$

2) If $G/N_{1}\cong G/N_{2}$ then $N_{1}\cong N_{2}$.

Thanks for the help.

Answer 1

Hint: Take $G=\mathbb{Z}_4\times \mathbb{Z}_2$. This group provides a basis for counter-examples to both of your statements.