A dielectric metasurface supporting a variety of quasi-bound states in the continuum (qBICs), including the intricate dark toroidal dipole and toroidal quadrupole Mie modes, is theoretically and experimentally investigated in the near-infrared. The metasurface consists of square slots etched into a thin silicon layer and periodically arrayed in a subdiffractive lattice residing on a sapphire substrate. The modal properties of the qBICs, i.e., the quality factors alongside the near- and far-field characteristics, are comprehensively assessed through a set of theoretical tools, including eigenfrequency simulations and multipolar expansion analysis. The results are corroborated by experimental studies verifying the existence of the qBICs. The investigated metasurface may serve as an ideal platform for nonlinear applications, such as third-harmonic generation, when leveraging the Kerr effect of silicon, as well as for lasing when the slot is filled with a low-index material hosting organic dye molecules.