We investigate simultaneous inter- and intra-group conflict in the shadow of within-group power asymmetry and complementarity in members' group-conflict efforts. A more symmetric group faces a higher degree of internal conflict, and might expend more effort in external conflict when the group-conflict effort technology is highly complementary. Depending on the degree of complementarity, the stronger player's relative contribution to external conflict might be higher in a more asymmetric group and, as a result, it is possible for the weaker player to earn a higher payoff. In the absence of any complementarity, the rent-dissipation is non-monotonic with the within-group power asymmetry.