Planning the trajectory of the controlled ego vehicle is a key challenge in automated driving. As for human drivers, predicting the motions of surrounding vehicles is important to plan the own actions. Recent motion prediction methods utilize equivariant neural networks to exploit geometric symmetries in the scene. However, no existing method combines motion prediction and trajectory planning in a joint step while guaranteeing equivariance under roto-translations of the input space. We address this gap by proposing a lightweight equivariant planning model that generates multi-modal joint predictions for all vehicles and selects one mode as the ego plan. The equivariant network design improves sample efficiency, guarantees output stability, and reduces model parameters. We further propose equivariant route attraction to guide the ego vehicle along a high-level route provided by an off-the-shelf GPS navigation system. This module creates a momentum from embedded vehicle positions toward the route in latent space while keeping the equivariance property. Route attraction enables goal-oriented behavior without forcing the vehicle to stick to the exact route. We conduct experiments on the challenging nuScenes dataset to investigate the capability of our planner. The results show that the planned trajectory is stable under roto-translations of the input scene which demonstrates the equivariance of our model. Despite using only a small split of the dataset for training, our method improves L2 distance at 3 s by 20.6 % and surpasses the state of the art.