Suspended-membrane 19-missing-hole microcavities in triangular lattice photonic crystals are numerically modeled by a three-dimensional finite-difference time-domain method. The resonance frequencies and the quality factors are calculated by interpolation of the discrete Fourier transformation series of the field with a Padé polynomial. The numerical results are compared with the photoluminescent spectra measured on the cavity of a nearly identical dimension. The symmetry properties of the defect modes are analyzed with the group theory, and resonance modes in the photonic-crystal cavities are identified as irreducible representations of the C_6v point group. The far-field radiations of the identified modes in the free space are also calculated by use of a vector Green's function. It is found that the numerical results agree very well with the experimental measurement in various aspects.