  We compute a certain index for an N=4 Chern-Simons theory with gauge group
U(N)^r in the large N limit with taking account of monopole contribution, and
compare it to the corresponding multi-particle index for M-theory in the dual
geometry AdS_4 x X_7. The internal space X_7 has non-trivial two-cycles, and
M2-branes wrapped on them contribute to the multi-particle index. We establish
one-to-one map between r-1 independent magnetic charges on the gauge theory
side and the same number of charges on the gravity side: the M-momentum and r-2
(=b_2(X_7)) wrapping numbers. With a certain assumption for the wrapped
M2-brane contribution, we confirm the agreement of the indices for many sectors
specified by the r-1 charges by using analytic and numerical methods.
