Switching device for a gearbox of a motor vehicle, having an actuation lever, which can optionally be a) transferred into a first shift gate in which it is mechanically coupled to a transmission component for actuating a switching cable pull or a gear shift linkage, or b) transferred into a second shift gate in which it is decoupled form the transmission component, wherein the transmission component is mounted in a movable manner, and wherein an arresting means embodied as a spring element is provided c) by means of which the transmission component can be fixedly attached in such a manner, that the transmission component does not apply any force to the switching cable pull or the gear shift linkage as long as the actuation lever is transferred into the second shift gate, and d) which is received inside an arresting reception area when the actuation lever is in the second shift gate, wherein the arresting reception area has an end centering in which the arresting means embodied as a spring element is received with a shaped part when the actuation lever is in the second shift gate, wherein the arresting reception area further has a releasing centering, wherein the releasing centering extends conically in the direction of the end centering and conically in the direction away from the end centering, wherein the shaped part has a cross section that is formed in such a manner that it can be received by the releasing centering in a form-fitted manner at least in certain areas when being moved out of the end centering, wherein the releasing centering and/or the end centering have surfaces at which the shaped part can be transferred in a self-acting manner into the end centering of the arresting reception area that is embodied as a target position for the arresting means by a restoring force of the arresting means embodied as a spring element that is acting in the direction of the end centering and that is applied to the arresting means when the actuation lever is in the second shift gate, characterized in that the actuation lever has an actuation projection by means of which the arresting means can be brought out of mesh with the arresting reception area with its shaped part during the transfer of the actuation lever from the second into the first shift gate. a) transferred into a first shift gate in which it is mechanically coupled to a transmission component for actuating a switching cable pull or a gear shift linkage, or b) transferred into a second shift gate in which it is decoupled form the transmission component, wherein the transmission component is mounted in a movable manner, and wherein an arresting means embodied as a spring element is provided c) by means of which the transmission component can be fixedly attached in such a manner, that the transmission component does not apply any force to the switching cable pull or the gear shift linkage as long as the actuation lever is transferred into the second shift gate, and d) which is received inside an arresting reception area when the actuation lever is in the second shift gate, wherein the arresting reception area has an end centering in which the arresting means embodied as a spring element is received with a shaped part when the actuation lever is in the second shift gate, wherein the arresting reception area further has a releasing centering, wherein the releasing centering extends conically in the direction of the end centering and conically in the direction away from the end centering, wherein the shaped part has a cross section that is formed in such a manner that it can be received by the releasing centering in a form-fitted manner at least in certain areas when being moved out of the end centering, wherein the releasing centering and/or the end centering have surfaces at which the shaped part can be transferred in a self-acting manner into the end centering of the arresting reception area that is embodied as a target position for the arresting means by a restoring force of the arresting means embodied as a spring element that is acting in the direction of the end centering and that is applied to the arresting means when the actuation lever is in the second shift gate, characterized in that the actuation lever has an actuation projection by means of which the arresting means can be brought out of mesh with the arresting reception area with its shaped part during the transfer of the actuation lever from the second into the first shift gate.