The results of a pseudopotential local-orbital calculation on the recently synthesized hybrid of graphite and hexagonal BN, BC2N, are presented. Three possible atomic arrangements in the BC2N monolayer, representing a variety of nearest-neighbor environments, are studied. For the monolayer structures considered, the one which maximizes chemical bond strength has the lowest total energy. The electronic structures of the three models are also investigated, and a correlation between the structural symmetries and the conducting properties of the models is found. In particular, the two structures which lack inversion symmetry are found to have semiconducting gaps, while the one with inversion symmetry is found to be metallic. This behavior is similar to the relation of graphite to BN. Of the inspected structures, the one with the lowest energy displays a local-density-approximation (LDA) gap of about 1.6 eV, which is expected to decrease upon stacking of the semiconducting monolayers.