In order to optimize the bulkiness of a primary structure of an aircraft engine attachment pylon and thus make it easier to install under the wing and as close as possible to the pressure face thereof, the disclosure herein provides an assembly in which the engine comprises a rear part arranged under a wing element equipped with a wing box, the primary structure being made up of the following independent elements: a first and a second side beam arranged one on each side of a vertical mid-plane of the engine; and an intermediate structure through which the vertical mid-plane of the engine passes and which is situated some distance from each of the first and second side beams.