I think it is an easy question, but for some reasons I am confused. Thank you for your help! Let $G$, $H_1$ and $H_2$ be finite groups. If
$G/H_1\cong G/H_2$, is it true that $H_1\cong H_2$?
If not, do you know a counterexample?
Thank you!
I think it is an easy question, but for some reasons I am confused. Thank you for your help! Let $G$, $H_1$ and $H_2$ be finite groups. If
$G/H_1\cong G/H_2$, is it true that $H_1\cong H_2$?
If not, do you know a counterexample?
Thank you!