Is it true that for any $n\in \mathbb{Z}$ with $n\geq 6$ and $n$ not a prime there exists a non abelian group of order $n$? How can we prove it?

If the answer to the above is negative is it maybe true that there are for any $p$ prime and $n$ positive integer grower than $3$ a non abelian group of order $p^n$?