**SPOILERS***
(The red herrings are: Exeter, Hertford, Lincoln, Pembroke (oxford colleges) - but this would leave 'Clare' ungroupable)
Kings, Queens, Jack, Ace (also Club but not really) - Playing Card values/types - but this would also leave 'Clare' ungroupable).
Pembroke, Exeter, Lincoln, Durham (Cathedral cities, would leave Hertford unpaired though unless you did oxford colleges, which would leave Clare ungroupable).

Wtf is a car club?

Car clubs are where different drivers share the same car - see 'carsharing' on wikipedia. It's a British-English word.