Total number of non isomorphic groups of order 122. Let $G$ be group of order $122 = 61 \cdot 2  = p \cdot q$ , where $p < q$ are primes. I know that there exists a unique non abelian group of order $pq$ and one abelian non isomorphic group of order $pq$. I think here are two non isomorphic of order $122$.
Please check my answer, it is right or not.

By Cauchy, $G$ has a (cyclic) subgroup $N$ of order $61$, which has index $2$ and hence is normal. Also $G$ has an element of order 2, whence a subgroup $H$ of order $2$, $G=HN$ and $H \cap N=1$. So $G$ is either a direct or semi-direct product of $H$ and $N$.
