We analyse the kinematics of disc stars observed by the RAdial Velocity Experiment (RAVE) survey in and beyond the solar neighbourhood. We detect significant overdensities in the velocity distributions using a technique based on the wavelet transform. We find that the main local kinematic groups are large-scale features, surviving at least up to ∼1 kpc from the Sun in the direction of antirotation, and also at below the Galactic plane. We also find that for regions located at different radii than the Sun, the known groups appear shifted in the vR–vφ velocity plane. For example, the Hercules group has a larger azimuthal velocity for regions inside the solar circle and a lower value outside. We have also discovered a new group at in the solar neighbourhood and confirmed the significance of other previously found groups. Some of these trends detected for the first time are consistent with dynamical models of the effects of the bar and the spiral arms. More modelling is required to definitively characterize the non-axisymmetric components of our Galaxy using these groups.