We studied the anharmonic modal contributions to heat transfer at the interface of crystalline Si and amorphous SiO2 using the recently proposed interface conductance modal analysis (ICMA) method. Our results show that ~74% of the thermal interface conductance (TIC) arises from the extended modes, which occupy more than ~58% of the entire population of vibrational modes in the system. More interestingly, although the population of purely localized and interfacial modes on the SiO2 side is less than 6 times the population of partially extended modes, the contribution to TIC by these localized modes is more than twice that of the contribution from partially extended modes. Such an observation, once again proves the nonnegligible role of localized modes to facilitate heat transfer across systems with broken symmetries, and reiterates the fact that neglecting the contribution of localized modes in any modal analysis approach is an over-simplification of the actual mechanisms of heat transfer. Correctly pinpointing the modal contributions is of vital importance, since these values are directly utilized in determining the temperature dependent TIC, which is crucial to silicon on insulator (SOI) technologies with myriad applications such as microelectronics and optoelectronics.