It is known that there are -up to conjugation- 5 classes of discrete subgroups of SU(2). One way to show this is by means of the McKay correspondence. My question is more regarding products of $SU(2)$, say with $n$ factors. Well, since I am definitely not familiar with the correspondence above, I would like to ask whether I have any hope to classify all finite subgroups of the product of 2 or 3 copies of $SU(2)$ by following the same line of thought. Or in case someone knows a more economical alternative, I would be very happy to listen to it.