Pump group for a cooling circuit of the motor of a vehicle, comprising: - an impeller rotatable around an axis (X-X) and an impeller shaft, which extends along said axis (X-X) and comprises an impeller end on which the impeller is mounted integral in rotation and an impeller shaft joint end opposite to the impeller end; - a mechanical drive and a mechanical shaft which extends along said axis (X-X), and comprises a mechanical shaft joint end, the mechanical shaft being rotatable by the mechanical drive and operatively connected to the impeller shaft; - an electric drive and an electric shaft which extends along said axis (X-X), and comprises a electric shaft joint end, the electric shaft being rotatable by the electric drive and operatively connected to the impeller shaft wherein the electric drive comprises an electric motor; the pump group being characterized by the fact that also comprises: - a joint group comprising respectively the impeller shaft joint end, the mechanical shaft joint end and the electric shaft joint end, and a first one-way coupling that operatively connects the impeller shaft joint end with the mechanical shaft joint end and a second one-way coupling that operatively connects the impeller shaft joint end with the electric shaft joint end; wherein the impeller shaft joint end is hollow and defines therein an impeller shaft housing suitable to house: - the second one-way coupling and electric shaft joint end, wherein the impeller shaft joint end supports on the outside the first one-way coupling and the mechanical shaft joint end, the latter defining a mechanical shaft housing; or - the first one-way coupling and the mechanical shaft joint end, wherein the impeller shaft joint end supports on the outside the second one-way coupling and the electric shaft joint end, the latter defining an electric shaft housing. - an impeller rotatable around an axis (X-X) and an impeller shaft, which extends along said axis (X-X) and comprises an impeller end on which the impeller is mounted integral in rotation and an impeller shaft joint end opposite to the impeller end; - a mechanical drive and a mechanical shaft which extends along said axis (X-X), and comprises a mechanical shaft joint end, the mechanical shaft being rotatable by the mechanical drive and operatively connected to the impeller shaft; - an electric drive and an electric shaft which extends along said axis (X-X), and comprises a electric shaft joint end, the electric shaft being rotatable by the electric drive and operatively connected to the impeller shaft wherein the electric drive comprises an electric motor; - a joint group comprising respectively the impeller shaft joint end, the mechanical shaft joint end and the electric shaft joint end, and a first one-way coupling that operatively connects the impeller shaft joint end with the mechanical shaft joint end and a second one-way coupling that operatively connects the impeller shaft joint end with the electric shaft joint end; - the second one-way coupling and electric shaft joint end, wherein the impeller shaft joint end supports on the outside the first one-way coupling and the mechanical shaft joint end, the latter defining a mechanical shaft housing; or - the first one-way coupling and the mechanical shaft joint end, wherein the impeller shaft joint end supports on the outside the second one-way coupling and the electric shaft joint end, the latter defining an electric shaft housing.