Housing of an electric machine, comprising a hollow cylindrical housing element, in particular a housing jacket, and at least one housing cover attached to an end of the housing element, wherein a cooling channel is formed in the housing, wherein the housing element has at least two cooling channel sections (8.1) of the cooling channel, which cooling channel sections (8.1), starting from a respective channel end opening in an end face of the housing element, extend into the housing element in an axial direction relative to a housing axis, wherein two adjacent cooling channel sections (8.1) are fluidically connected to each other via a deflection section (8.2) formed in the housing cover, wherein a gasket for sealing off the cooling channel is arranged between the housing element and the housing cover, wherein the gasket has through-openings, in the region of the channel end openings, for directing the cooling channel into the housing cover, and wherein the gasket has a ring-shaped support and a sealing assembly arranged on the support, characterized in that - the sealing assembly encloses the support in such a way that the support is completely sealed off from the cooling channel of the housing, - the support has an inner ring and an outer ring, and also webs connecting inner ring and outer ring, wherein the inner ring, the outer ring and the webs are preferably formed in one piece, - the sealing assembly has a first layer thickness over the inner ring and/or over the outer ring, wherein the sealing assembly has the first layer thickness over a first group of the webs and a second layer thickness over a second group of the webs, wherein the second layer thickness is smaller than the first layer thickness, - the sealing assembly forms, on the webs of the first group, a sealing surface for sealing off adjacent cooling channel sections (8.1), and forms, on the webs of the second group, a connection surface for connecting adjacent cooling channel sections (8.1). wherein a cooling channel is formed in the housing, wherein the housing element has at least two cooling channel sections (8.1) of the cooling channel, which cooling channel sections (8.1), starting from a respective channel end opening in an end face of the housing element, extend into the housing element in an axial direction relative to a housing axis, wherein two adjacent cooling channel sections (8.1) are fluidically connected to each other via a deflection section (8.2) formed in the housing cover, wherein a gasket for sealing off the cooling channel is arranged between the housing element and the housing cover, wherein the gasket has through-openings, in the region of the channel end openings, for directing the cooling channel into the housing cover, and wherein the gasket has a ring-shaped support and a sealing assembly arranged on the support, characterized in that - the sealing assembly encloses the support in such a way that the support is completely sealed off from the cooling channel of the housing, - the support has an inner ring and an outer ring, and also webs connecting inner ring and outer ring, wherein the inner ring, the outer ring and the webs are preferably formed in one piece, - the sealing assembly has a first layer thickness over the inner ring and/or over the outer ring, wherein the sealing assembly has the first layer thickness over a first group of the webs and a second layer thickness over a second group of the webs, wherein the second layer thickness is smaller than the first layer thickness, - the sealing assembly forms, on the webs of the first group, a sealing surface for sealing off adjacent cooling channel sections (8.1), and forms, on the webs of the second group, a connection surface for connecting adjacent cooling channel sections (8.1). - the sealing assembly encloses the support in such a way that the support is completely sealed off from the cooling channel of the housing, - the support has an inner ring and an outer ring, and also webs connecting inner ring and outer ring, wherein the inner ring, the outer ring and the webs are preferably formed in one piece, - the sealing assembly has a first layer thickness over the inner ring and/or over the outer ring, wherein the sealing assembly has the first layer thickness over a first group of the webs and a second layer thickness over a second group of the webs, wherein the second layer thickness is smaller than the first layer thickness, - the sealing assembly forms, on the webs of the first group, a sealing surface for sealing off adjacent cooling channel sections (8.1), and forms, on the webs of the second group, a connection surface for connecting adjacent cooling channel sections (8.1).