The GaN planar hexagonal microcavities are grown by the selective vapor-phase epitaxy technique. The spectra are measured by the low-temperature cathodoluminescence method using a scanning electron microscope. The obtained spectra show a huge Rabi splitting (similar to 100 meV). Numerical simulation of the spatial distribution of the intensities of modes in a hexagonal cavity is carried out. Certain modes can have a high spatial localization leading to strong coupling with the exciton and huge Rabi splitting. The fraction of excitons in polariton modes, which correlates with the intensity of exciton radiation associated with these modes, is theoretically calculated for hexagonal-shaped microcavities. Thus, the form of the dependence of the radiation probability on the eigenfrequencies of the structure is obtained.