With the special requirements of on-board switching for satellite communications, the divide-and- conquer dispatching scheme is proposed based on Memory-Space-Memory (MSM) Clos network switches. By introducing the notion of colliding fields, the matching for a Clos-network is simplified to the problem of how to select cells for central modules within a colliding field, which restricts the scope of collisions, and reduce the complexity of the dispatching. This dispatching scheme has low hardware complexity, and can achieve high performance under various traffic models. Simulation results show that divide-and-conquer dispatching scheme approaches 100% throughput under all the traffic conditions, and has a very low delay, which meets the requirements of satellite communication.