In this paper, we explore the discovery of latent symmetries of data in a self-supervised manner. By considering sequences of observations undergoing uniform motion, we can extract a shared group transformation from the latent observations. In contrast to previous work, we utilize a latent space in which the group and orbit component are decomposed. We show that this construction facilitates more accurate identification of the properties of the underlying group, which consequently results in an improved performance on a set of sequential prediction tasks.