By point group I mean a finit subgroup of $\mathrm O(\Bbb R^n)$.
Lists of point groups for some small dimensions are found on Wikipedia, but I am not certain about their completeness. As there seem to exist lists, I wonder the following:
Question: How would one go about classifying the point groups in some fixed dimension $n$?
I know that all (finite) reflection groups can be listed systematically via Coxeter diagrams, but not all point groups are reflection groups $-$ in fact, they are not even subgroups of reflection groups as explained in this answer.
Can the classification of point groups be obtained from the classification of reflection groups in some simple way, e.g. by only taking products and subgroups?