Motivating factor behind this question is the comments which are given for this question asked some hours ago http://math.stackexchange.com/questions/6538/group-of-order-105
So given a group $G$ of order $n$ what are the different methods for constructing a non abelian group of order $n$. Well, i have seen a method which Herstein uses in his book. He takes a cyclic group of given order and defines an Automorphism on the cyclic group and then places some restrictions.
I would like to know, whether there are anymore methods for obtaining a Non Abelian group of a given order.