Example for subgroups $H$ and $K$ where $HK = K H$ and neither $H$ nor $K$ is normal?

Question

Let $G$ be a finite group with proper non-trivial subgroups $H$ and $K$.

If $H K = K H$, then $H K$ is obviously a subgroup of $G$. It is well-known that $H$ or $K$ being normal implies that $H K$ is such a subgroup.

Question: Is there a finite group $G$ with proper non-trivial subgroups $H$ and $K$ such that $H K = K H$ and neither $H$ nor $K$ is normal in $G$?

Answer 1

Example In $D_4$ $H=<s>$,$K=<r^2s> $ Clearly HK is subgroup of G But None of H and K is normal subgroup.