Superconductivity in alkali-intercalated iron selenide, with T_{c}'s of 30K and above, may have a different origin than that of the other Fe-based superconductors, since it appears that the Fermi surface does not have any holelike sheets centered around the Γ point. Here we investigate the symmetry of the superconducting gap in the framework of spin-fluctuation pairing calculations using density functional theory bands downfolded onto a three-dimensional (3D), ten-orbital tight-binding model, treating the interactions in the random-phase approximation (RPA). We find a leading instability towards a state with d-wave symmetry, but show that the details of the gap function depend sensitively on electronic structure. As required by crystal symmetry, quasinodes on electron pockets always occur, but are shown to be either horizontal, looplike, or vertical depending on details. A variety of other 3D gap structures, including bonding-antibonding s-symmetry states which change sign between inner and outer electron pockets, are found to be subdominant. We then investigate the possibility that spin-orbit coupling effects on the one-electron band structure, which lead to enhanced splitting of the two M-centered electron pockets in the 2-Fe zone, may stabilize the bonding-antibonding s_{±}-wave states. Finally, we discuss our results in the context of current phenomenological theories and experiments.