  We analyze the superconformal index of the N=3 supersymmetric Z_k generalized
orientifold theories recently proposed. In the large N limit we derive the
index from the Kaluza-Klein modes in AdS_5 x S^5/Z_k, which are obtained from
ones in AdS_5 x S^5 by a simple projection. For the ordinary Z_2 orientifold
case the agreement with the gauge theory calculation is explicitly confirmed,
and for Z_k with k > 2 we perform a few consistency checks with known results
for N=3 theories. We also study finite N corrections by analyzing wrapped
D3-branes and discrete torsions in the dual geometry.
