counting – How to sort a list containing products

I’ve some difficulties with lists containing products as elements, e.g. list = {ABA, AKB, AKR}, where A and B are from the same ‘family’, let’s call it sector 1, while K and R are from sector 2.

I would like to find a way to sort the list according to the occurrence of elements from sector 2.

The desired output should be something like

listWith0Sector2elements = {AKB}
listWith1Sector2elements = {AKB}
listWith2Sector2elements = {AKR}

my naive attempt (Count, MemberQ…) unfortunately failed, as I have never had anything to do with products