System for fixing a rail and adapter piece for such a system

System for fixing a rail onto a foundation comprising:

• a spring element, which can be clamped against the foundation by means of a clamping element, wherein the spring element has at least one spring arm;
• and
• an adapter piece, which has a holder, in which an end section of the spring arm of the spring element sits, wherein the adapter piece has a contact surface section formed at its periphery, with which, when the system is assembled, it sits on the rail foot of the rail to be fixed, such that the elastic retaining force exerted by the spring element is transferred onto the rail foot;
• and
• wherein the adapter piece is rotatably mounted on the end section of the spring arm about a rotary axis, such that the adapter piece has at its periphery at least two contact surface sections, one of which, depending on the rotary position of the adapter piece, in each case lies against the rail foot, and such that one contact surface section of the adapter piece has a greater distance from the rotary axis of the adapter piece than the other contact surface section.