A container for receiving cryogenic media and/or units which are to be stored at low temperatures, having an outer shell (1) and an insulating shell (10) which is connected directly or indirectly to said outer shell (1) in a positionally stable manner and is optionally surrounded by one or more further insulating shells (10), wherein an inner shell (2) for storing cryogenic media is connected to the outer shell (1) via fastening elements (3) in a positionally stable manner. Each insulating shell (10) is of at least two-part configuration and is fastened to the outer shell (1) and/or to the inner shell (2) by positioning elements (11, 26, 27) which are independent of the fastening elements (3), wherein the insulating shell (10) is spaced apart without contact from the outer or inner shell (1,2) or from a further insulating shell (10) with the formation of a gap (15).