Such a mounting device is known from U.S. Pat. No. 3,579,840. Therein, in each case a fixed clamping jaw as well as an adjustable clamping jaw on the opposite side are arranged on a ring-shaped holding device. On the bottom side of the ring-shaped holding device, between the two clamping jaws, a bar-shaped recoil cleat is provided for the engagement in a corresponding continuous transverse groove on a base portion which can be attached to the handgun. By means of the recoil cleat, the forces acting at the time of the firing are absorbed, and as a result an improved precision can be achieved. However, as a result of the continuous transverse grooves, the attachment device is also weakened, and thus the stiffness is affected.