I know how to count number of non isomorphic group in case of abelian case by Fundamental theorem of abelian case .
I am interested in how to count non abelian non isomorphic group. I don't know is it possible or not?
But many examples (of small order ) are asked in exercise to find that. I am using observation about possible non abelian group. Many time some group remain to be un counted.
For example: Group of order $8$. So there $3$ abelian group $Z_8$,$Z_4\times Z_2$,$Z_2\times Z_2\times Z_2$, and Non abelian group of $D_4 $ and $ Q_8$.
How to guarantee that our listing is complete or some group had to be mention?