Extraordinary optical transmission (EOT) behaviour is investigated in a subwavelength plasmonic nanostructure, consisting of a gold film perforated with a square nanohole array and deposited on a silicon dioxide substrate. The essential aspect of the proposed structure is the periodic disorder that enables broadband transmission peaks in the visible and near-infrared region and reduces the structure's size, which mainly arises from the excitation of localized surface plasmon resonances (LSPRs). Optical cavity modes formed in the nanoholes and the hybridization of plasmon modes. Further, the performance of the proposed nanostructure as a plasmonic sensor is analyzed by increasing the index of refraction of the local environment; the EOT exhibit remarkable refractive index sensitivity of up to 944 nm/RIU, a figure of merit of 9.25 and a contrast ratio of 47% are realized. The proposed structure has some practical significance for designing low-cost and effective sensing devices.