Let $G$ be a finite subgroup of the group of automorphsims of a $K3$ surface $S$.
Consider the quotient $S/G$. 

I am interested in the collection of such qutients:


$$\{ S/G \mid S\text{ is a K3 surface, }G\text{ is a finite subgroup of }Aut(S) \}$$

Is there any classification result for the collection of quotients?

What if I assume that $G$ contains an involution that acts on $H^{2,0}(S)$ as multiplication by $-1$.
Is the collection finite up to deformation?