In $D_4$, find $H_1$ isomorphic to $\mathbb{Z}_4$ and $H_2$ isomorphic to the Klein Four Group with $D_4/H_1$ isomorphic to $D_4/H_2$.

Question

a) In $D_4$, find $H_1$ isomorphic to $\mathbb{Z}_4$ and $H_2$ isomorphic to $V$, the Klein Four group, with $D_4/H_1$ isomorphic to $D_4/H_2$.

b) In $D_4$, find subgroups $H$ and $K$ with $H$ normal in $K$ and $K$ normal in $D_4$ but $H$ not not normal in $D_4$.

-and in this I'm just confused.