A new ice phase, ice XIX, was discovered in 2018, and is the second hydrogen-ordered polymorph of hydrogen-disordered ice VI. The first hydrogen-ordered polymorph of ice VI is ice XV, and ices XIX, VI, and XV comprise a unique triplet group in the ice family. However, the exact crystal structure of ice XIX has not been confirmed. We constructed four possible conformations of ice XIX using neutron diffraction data obtained by Gasser et al. We then optimized these structures and simulated their Raman scattering spectra using first-principles density functional theory. By comparing these simulated spectra with the experimental Raman scattering spectra, we were able to exclude the existence of a ferroelectric structure with the space group Cc. The other three candidate structures are in good agreement with the experimental Raman scattering data; two of them are ferroelectric structures with the space group P21; and the last one is a weak ferroelectric structure with the space group Cc. We proposed that the partially hydrogen-ordered structure of ice XIX maybe a mixing of several hydrogen-ordered structures.