The GaN planar hexagonal microcavities were grown by a selective vapor phase epitaxy. The spectra were measured by the low-temperature cathodoluminescence method in-situ scanning electron microscope. The obtained spectra show a huge Rabi splitting (in order of 100 meV). Numerical simulation of the spatial distribution of the modes’ intensities of a hexagonal resonator is shown. Some modes can have strong spatial localization, leading to strong coupling with the exciton and huge Rabi splitting. Theoretically, we calculated the fraction of excitons in polariton modes, which correlates with the intensity of exciton radiation associated with these modes, for microcavities of a hexagonal shape. Thus, we have obtained the form of the dependence of the radiation probability on the eigenfrequencies of the structure.