Behavioral scientists often examine the relationships between two or more latent variables or constructs (e.g., attitudes, emotions), and Structural Equation Modeling (SEM) is the state-of-the-art for doing so. When comparing these structural relations among many groups, they likely differ across the groups. However, it is equally likely that some groups share the same relations, and that clusters of groups emerge in terms of the relations between the latent variables. For validly comparing the latent variables’ relations among groups, it is important to remember that such variables are indirectly measured via questionnaires and that one should evaluate whether this measurement is invariant across the groups (i.e., measurement invariance). In the case of many groups, often at least some parameters differ across the groups. Current clustering methods using SEM (i.e., mixture SEM methods) force all SEM model parameters (i.e., measurement parameters, structural relations, etc.) to be equal within a cluster, thus also capturing similarities and differences in measurement, which are unrelated to the research question. We propose mixture multigroup SEM (MMG-SEM) to obtain a clustering of groups focused entirely on the structural relations by making them cluster-specific, while allowing for the measurement parameters to be (partially) group-specific to account for measurement non-invariance. In this way, MMG-SEM disentangles differences in structural relations from differences in measurement parameters. We present an evaluation of MMG-SEM’s performance in terms of recovering the group-clustering and the group- and cluster-specific parameters as well as an evaluation of different approaches to select the number of clusters (e.g., AIC, BIC, etc.).