We propose an optimized high-quality (Q)-factor silicon nitride (SiN)-based planar photonic crystal (PhC) cavity on a silicon-on-insulator (SOI) substrate, specially tailored for integrated photonics in the visible-wavelength range. The cavity is in the centre of a SiN planar PhC that consists of a triangular lattice from which three holes are removed, i.e., the three-missing-holes point defect (L3). We detail the optimization of the geometrical parameters of the PhC membrane and show how they can affect the band gap width. Moreover, we investigate the enhancement of the Q-factor by tuning the position and radius of the lateral, upper, and lower boundary holes near the cavity edge. We demonstrate that the calculated Q-factor for the designed cavity increases by a factor of 12 relative to that for a cavity without displaced and reduced air holes, while the calculated mode volume remains almost constant. These high-Q-factor structures would be advantageous in integrated sensing devices.