A housing having an overpressure protection includes a pressure relief opening with a diaphragm sealing plug to be closed in a fluid-tight manner. The diaphragm sealing plug has a central portion and an angled free peripheral portion. The free peripheral portion in the non-pressurized operating state extends away from the central portion in the direction of the housing external side. The central portion, by way of an increasing housing internal pressure in the axial direction, is deformable in such a manner that the peripheral portion by way of a tension stress that is derived from the deformation of the central portion in a manner proportional to the pressure is releasable from the housing wall in the axial direction in a progressive manner from the inside to the outside such that the diaphragm sealing plug releases the pressure relief opening when a predefined maximum housing internal pressure is reached or exceeded.