In this paper, we seek to identity how mathematical and economic analysis can be used to gain insights about the mutation of social groups. Group mutability has been studied in multiple domains, with insights generated on significant factors at differing scales. Mathematical modeling enables the simultaneous study of such phenomena, understanding interactions and generating hypotheses for experiments. In particular, we focus on group fracture, where individuals leave groups of which they are members. For example, this can be due to perceived differences with other group members due to norm related conflict (such as extreme actions by some members). Our aim is to consider simple mathematical models incorporating a selection of social and psychological theory which describes these phenomena as a way to understand their interplay, and describe the trade-offs and challenges. This will help a federation model the behavior of extremist groups, and determine not only when an intervention is necessary, but also the best course of action to take to induce the fracture of such groups. This paper is an exploratory investigation into methods of achieving this goal and evaluating the usefulness of the outputs to federations.