With this rank there is very less chances of getting seat in any good law college but then too you can always apply in some private college which accept CLAT score. Below is the list of some college which you can look into - 

• Narsee Monjee Mumbai - Rank- 6000
• UPES Dehradun - Rank- 8000
• KIIT Bhubaneshwar - Rank- 8000
• other private law colleges - rank - 10000-25000

Hey.
Here is a list of NLUs and their respective cut offs for the general category for admission through CLAT in the previous year. You can expect a similar range of cut off ahead too. Considering a rank of 6676, if you belong to the general category your chances are not much.

National Law School of India University
66
National Academy of Legal Studies and Research
135
National Law Institute University
386
West Bengal National University of Judicial Sciences
260
National Law University Jodhpur
376
Hidayatullah National Law University
657
Gujarat National Law University
494
Ram Manohar Lohiya National Law University
668
Rajiv Gandhi National University of Law
924
Chanakya National Law University
1186
National University of Advanced Legal Studies
928
National Law University Odisha
1167
National University of Study and Research in Law
1255
National Law University and Judicial Academy
1556
Tamil Nadu National Law School
1571
Damodaram Sanjivayya National Law University
1432
Maharashtra National Law University, Mumbai
503
Maharashtra National Law University, Nagpur
1532
Maharashtra National Law University, Aurangabad
1588
You can go for private colleges accepting CLAT scores for admission instead.
There are various Private Colleges that accept CLAT scores other than the National Law Universities. Here is a list of a few of them.

Jindal Global Law School, Sonepat
Kirit P. Mehta School of Law, Mumbai
NIRMA UNIVERSITY, Ahmedabad
ICFAI Law School, HyderabadSchool of Law, GITAM University, Visakhapatnam
Alliance School of Law, Bangalore
IFIM Law College, Bangalore
LLOYD Law College,Greater Noida
Amity University, U.P.
Asian Law College, Noida
Manipal University, Jaipur

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