Anomaly detection has evolved as a successful research subject in the areas such as bibliometrics, informatics and computer networks including security-based and social networks. Almost all existing anomaly detection techniques have some limitations and do not focus specifically on detecting anomalous groups. Anomaly detection is also a crucial problem in processing large-scale datasets when our goal is to find abnormal values or unusual events. The authors decided to survey existing group anomaly detection techniques because there is a need to consider group anomalies for mitigation of risks, prevention of malicious collaborative activities, and other interesting explanatory insights by identifying groups that are not consistent with regular group patterns. In this research, we bifurcated group anomaly detection techniques into activity-based and graph-based methods. The graphical methodologies are then further classified under static versus dynamic and attributed versus plain graph methods. We have also listed the datasets used in various studies to detect group anomalies along with detected anomalies and the various performance measures used to validate the results. Towards the end, we have provided various applications of group anomaly detection and the research challenges that group anomaly detection presents to the scientific community and enlisted some of the future trends for this particular research area.