Find subgroups N and H of D4 such that N is normal H and H is normal to D4, but N is NOT a

normal subgroup of D4.

Well D4={e,r,r^2,r^3,f,fr, fr^2, fr^3}

I'm not really sure on all of the subgroups.

I have a couple:

{e,f}

{e,r,r^2,r^3}

I guess the biggest problem is finding the subgroups