The two-dimensional shallow water system over a rough bottom is considered. An overdetermined system of equations for finding the allowed symmetries is obtained. The consistency of this overdetermined system of equations is investigated. A general form of the solution of this system is obtained. The kernel of the symmetry operators is found. Cases where the kernel extensions of symmetry operators exist are presented. The corresponding classifying equations are given. The results of the group

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... ssification have indicated that the two-dimensional shallow water system above rough bottom cannot be linearized by point transformation in contrast to the one-dimensional shallow water system in cases of horizontal and inclined bottom profiles.