A large number of network applications today allow several users to interact together using the many-to-many service mode. In many-to-many communication, also referred to as group communication, a session consists of a group of users (we refer to them as members), where each member transmits its traffic to all other members in the same group. In this paper, we address the problem of many-to-many traffic grooming in WDM mesh networks. In this problem, a set of many-to-many session requests, each with an arbitrary subwavelength traffic demand, is given and the objective is to provision the sessions on the WDM network with the minimum network cost. The cost of a WDM network is dominated by the cost of higher-layer electronic ports (we refer to them as transceivers). Therefore, our objective is to minimize the total number of transceivers used. We address the problem in both nonsplitting networks, where the nodes do not have optical splitting capabilities, and in splitting networks, where the nodes do have optical splitting capabilities. First, we formulate the problem in each of the two networks as a mixed integer linear program (MILP). Afterwards, based on observations from optimal solutions, we develop a heuristic approach for each network by relaxing and simplifying its corresponding MILP. Through extensive experiments, we verify the accuracy of our proposed heuristics and also show when each of the two networks is a more cost-effective choice for many-to-many traffic grooming.