Projective image type (awaiting review)

The projective image of an Artin representation is a finite subgroup of $\PGL_n(\C)$. Possible subgroups have been classified for small $n$. The case which has garnered the most interest is when $n=2$, in which case the image is isomorphic to either $A_4$, $S_4$, $A_5$, or $D_n$ for some $n\geq 2$ (where $D_2$ is the Klein group).