DH turns out to be a lot like RSA, so bit lengths are comparable between the two and neither is directly comparable to symmetric ciphers like AES. A specific Diffie-Hellman exchange happens using some parameters: a generator for the base, and a prime to use as modulus. (An exponent remains secret.) DH Groups refer to specific, pre-chosen prime-and-generator pairs so that, for example, SSH can negotiate "group 14" instead of transferring the complete parameters themselves.
These groups have been standardized in RFC 2409, with additional groups defined in RFC 3526. The latter RFC defines the bit lengths of the groups explicitly, stating that group 5 is 1536 bits, group 14 is 2048, and group 16 is 4096 bits. As far as I can tell, groups 1 and 2 defined in the earlier RFC are only 768 and 1024 bits, respectively.
Note well: I believe this means DH groups 1 and 2 are dangerously short and should not be used to set up an IPSEC VPN today. Likewise, PuTTY should really be configured out-of-the-box to warn about the use of anything less than DH group 14.