By using first-principles calculations and symmetry analysis, we study the topologically nontrivial features of sextuple nodal-point phonons together with other kinds of topological phonons in realistic materials. The sextuple nodal-point phonons in all 230 space groups, enumerated in this paper, are localized at the boundaries of the three-dimensional Brillouin zone (BZ), and protected both by time-reversal symmetry ($\cal T$) and little-group symmetries. Moreover, in a realistic material sample of insulator SiO$_2$, we find that the sextuple nodal-point phonons exist at the high-symmetry point \emph{H} of the first BZ, and generate four-fold surface states. Interestingly, owing to the special crystal symmetries in SiO$_2$, triple nodal-point phonons and Dirac phonons exist at the point $\Gamma$ and \emph{P}, respectively, and exhibit exotic quadruple surface states. More than these, the topological phononic nodal links also appear around the point $\Gamma$, and exhibit drumhead like surface states in this material. Our theoretical work not only proposes an effective way to search for multi-fold topological phonons including Dirac phonons and sextuple nodal-point phonons, but also presents a realistic material sample to realize the coexistence of multiple nodal-point and nodal-link phonons.