Key having a retractable insert, and related insert-extending module

The invention relates to a retractable key comprising an upper half-shell (3) and a lower half-shell which are assembled together so as to form a housing, and an insert-extending module configured so as to be mounted in said housing. The insert-extending module includes: an insert pivotably mounted in the housing between a retracted position and an deployed position, a push button (8) axially projecting from the upper half-shell (3) so as to be axially pressed by a user and comprising a rotation-locking means (9) engaging with a corresponding rotation-locking means (10) of the housing, the rotation-locking means (9, 10) guiding the push button (8) in axial translation (A-A), an elastic return element, a first end of which is attached to the insert and a second end of which is attached to the push button (8) in order to urge the insert to pivot toward the extended position when the push button (8) is pressed, and a retaining means (17) supported by the push button (8) and engaging with a complementary retaining means (18) of a half-shell of the housing, said retaining means (17, 18) being configured so as to enable the axial translation (A-A) of the push button (8).