Counterfactual explanations assess unfairness by revealing how inputs must change to achieve a desired outcome. This paper introduces the first graph-based framework for generating group counterfactual explanations to audit group fairness, a key aspect of trustworthy machine learning. Our framework, FACEGroup (Feasible and Actionable Counterfactual Explanations for Group Fairness), models real-world feasibility constraints, identifies subgroups with similar counterfactuals, and captures key trade-offs in counterfactual generation, distinguishing it from existing methods. To evaluate fairness, we introduce novel metrics for both group and subgroup level analysis that explicitly account for these trade-offs. Experiments on benchmark datasets show that FACEGroup effectively generates feasible group counterfactuals while accounting for trade-offs, and that our metrics capture and quantify fairness disparities.