Constructing Non Abelian Groups of Given order The motivating factor behind this question is the comments given for this question asked some hours ago Group of order $105$
So, given a group $G$ of order $n$, what are 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.

Have you tried taking the semi-direct product of two subgroups (one needs to be a normal subgroup).  The order of G is the product of the orders of the subgroups.  One subgroup needs to be normal.  If the other is not, then the semidirect product is usually (if not always) non-abelian
