An efficient way to cope with the combinatorial explosion problem induced by the model checking process is to compute the Symbolic Observation Graph (SOG) which is a condensed representation of the state space graph based on a symbolic encoding of the nodes. Another way is to parallelize the construction/traversal of the state space on multiple processors. In this paper, we combine the two mentioned approaches by proposing three different approaches to parallelize the construction of the SOG. A multi-threaded approach based on a dynamic load balancing and a shared memory architecture, a distributed approach based on a distributed memory architecture and a hybrid approach that combines the two previous approaches.