In recent decades, research about surface plasmon polariton (SPP) has earned its popularity in nanotechnology with many theoretical achievements, much progress in metal nanostructure manufacturing, spectral analyzing, biomedicine ultrasensing, etc. Group theory is an effective tool for analyzing the spectra of symmetrical organized multiparticles (dubbed as plasmonic metamolecule). Recently, SPP Fano resonance in nanostructure either from plasmonic metamolecules or from symmetry-breaking has attracted much attention. Regarding to the subgroup decomposition analysis of the D3h and D4h plasmonic metamolecule surface plasmon resonance spectra and the mechanism of forming the Fano resonance spectral dip, this paper proposes an explanation method based on group theory.By using a similar group theory approach to constructing the molecular vibration normal modes, the method to build the dipolar SPP symmetric modes of plasmonic metamolecules is established. It is confirmed that under the linear polarization excitation there exists only two dipolar SPP symmetric modes for a ring shaped Dnh plasmonic metamolecule, while adding the center particle will merely add an extra independent symmetric mode. For the D3h and D4h plasmonic metamolecule, it is found that there are two dominant eigenmodes i. e., one is composed by adding two symmetric modes and the other by subtracting two symmetric modes. The decomposition analysis further reveals that the negative coefficient of the symmetric mode for forming the short wavelength eigenmode for D3h tetramer plasmonic metamolecules is much smaller than that for D4h pentamer plasmonic metamolecules, thereby explaining that the Fano resonance dip of the pentamer is sharper than that of the tetramer. It is worth noting that the group theory can provide some guidance for building the symmetric modes and the SPP eigenmodes, but is unable to determine the coefficient of each symmetric mode.As for the origin of Fano resonance dip, so far there have existed two different perspectives: one is the traditional viewpoint, i.e., the Fano resonance dip is formed due to the coupling of the wideband superradiant bright mode with the narrowband subradiant dark mode, and the other is that the Fano resonance dip is formed by the destructive interference between two neighboring eigenmodes. The decomposition analysis described in this paper actually can unify these two perspectives.