Does anybody have an example of a normal subgroup N of a group $G\times H$ such that N is **not** equal to some product $N\_1\times N\_2$ while $N\_1$ is normal in G and $N\_2$ is normal in H.

I've already proofed the analog statement for rings-ideals, but I've understood that this is not necessary so using groups-normal subgroups and I'm having a hard time to find an example.