A beta subtype methylase, recognizes the double-stranded DNA sequence 5'-GCNNNNNNNGC-3', methylates C-2 on both strands, and protects the DNA from cleavage by the MwoI endonuclease. a 2'-deoxycytidine in DNA + S-adenosyl-L-methionine = an N(4)-methyl-2'-deoxycytidine in DNA + H(+) + S-adenosyl-L-homocysteine Belongs to the N(4)/N(6)-methyltransferase family. N(4) subfamily.