In this study, gold nanodisk clusters in heptamer orientations as clusters were used to design a super-heptamer consisting of one central and six peripheral heptamers. We examined the position and movement of the plasmon and Fano resonances by sketching the spectral response of the superstructure for various nanodisk dimensions. The quality of the interference between the superradiant and subradiant plasmon resonance modes of the nanodisk clusters was found to depend strongly on the structural configuration and the refractive index of the environmental medium. We replaced the central heptamer with a nanodisk and probed the position of the Fano resonance by geometrically altering the nanodisk structure. Finally, the effect of the dielectric environment on the plasmon response of both of the studied structures was examined numerically and theoretically. The localized surface plasmon resonance sensitivity of the finite plasmonic structures to the presence of liquid substances was investigated and shown by plotting the linear figure of merit. The finite-difference time-domain method was used as a numerical tool to investigate the plasmon response of the structure.