Networked control of discrete event systems is investigated in our previous papers. In a networked control, the communication between the plant and supervisor is via shared communication networks, where communication delays and losses are unavoidable. Network observability is introduced to characterizes the condition under which observation delays and losses will have no adverse effect on networked control. In this paper, we further investigate network observability in two aspects. The first aspect is to propose an algorithm to check network observability for a given specification language K. The idea is to calculate the language generated by a state-estimate-based supervisor which can be derived from the given K and then compare it with K. If they are equal, then K is network observable. The second aspect is to propose an algorithm to calculate a maximal network observable sublanguage of K if K is not network observable. The algorithm is to find a legal supervisor first and then try to enlarge it as much as possible. The language generated by the enlarged supervisor is maximal.