We have normal subgroups $ N$ and $ N'$ of a group $ G $. Is the following statement correct?  $G/N\cong G/N'\Leftrightarrow N\cong N'$.  $\Leftarrow $ is trivial.  $\Rightarrow:$ I don't know how to start. Or should I search for counter examples?  I would be pleased, if someone could give a hint.
I know it is possible for a group $G$ to have normal subgroups $H, K$, such that $H\cong K$ but $G/H\not\cong G/K$, but I couldn't think of any examples with $G$ finite. What is an illustrative example?
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