It is know 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 porducts of $SU(2)$ say with $n$ factors. Well, since I am definitely not familiar with the correspondence above, I would like to ask wheter I have any hope to classify all finite subgroups of 2 or 3 times $SU(2)$ by following the same line of thoughts. Or in case someone knows a more economical alternative, I would be very happy to listen to it.