Let F be a finite field and T a transcendental element over F. In this paper, we construct, for integers m and n relatively prime to the characteristic of F (T), infinitely many imaginary function fields K of degree m over F (T) whose class groups contain subgroups isomorphic to (Z / n Z)m. This increases the previous rank of m - 1 found by the authors in [Y. Lee, A. Pacelli, Class groups of imaginary function fields: The inert case, Proc. Amer. Math. Soc. 133 (2005) 2883-2889].