Let $G$ be a group such that $|G| = 2^2 \cdot 3^2$. I want to show that there exists a nontrivial normal subgroup of $G$.
My tries: By the Sylow theorem I find out that te number of $2$-Sylow subgroups is equal to 1,3 or 9. On the other side the number of $3$-Sylow subgroups is equal to $1$ or $4$. Now I don't have any ideas what to do.
