Sorting contacts and iCloud

When I used iTunes to keep my contacts synced, I could organize them into categories so I didn't have to have all of them sync to my phone. Now, with iCloud, I don't see a way to do that. I now have over 2000 contacts on my phone, and my car bluetooth is not handling it well. How can I organize them into groups so I can use my car's bluetooth again? (it basically gets 'confused' and tries to call the wrong person).

I know that I can create groups via the iCloud website, but there still doesn't seem to be a way to only sync certain groups...so I'm still looking at having 2000+ contacts on my phone.