Clutch module of electronic lock and electronic lock

The invention provides a clutch module of an electronic lock, which comprises a shell and is characterized in that the shell is provided with a lock cylinder connecting piece used for being connected with a mechanical lock cylinder or a switch knob, and the lock cylinder connecting piece can rotate between a locking position and an unlocking position; the first meshing tooth is connected with the lock cylinder connecting piece; the second meshing tooth is connected with the lock cylinder connecting piece; a reset member; the clutch is connected with the reset piece and provided with a damping device; the driving device is connected with the clutch, and the driving device comprises a driving state and a non-driving state; when the driving device is in a driving state, the driving device drives the clutch to be connected with the first meshing teeth or the second meshing teeth, and the driving device drives the first meshing teeth or the second meshing teeth to rotate so as to drive the lock cylinder connecting