This paper introduces the first graph-based framework for generating group counterfactual explanations to audit model fairness, a crucial aspect of trustworthy machine learning. Counterfactual explanations are instrumental in understanding and mitigating unfairness by revealing how inputs should change to achieve a desired outcome. Our framework, named Feasible Group Counterfactual Explanations (FGCEs), captures real-world feasibility constraints and constructs subgroups with similar counterfactuals, setting it apart from existing methods. It also addresses key trade-offs in counterfactual generation, including the balance between the number of counterfactuals, their associated costs, and the breadth of coverage achieved. To evaluate these trade-offs and assess fairness, we propose measures tailored to group counterfactual generation. Our experimental results on benchmark datasets demonstrate the effectiveness of our approach in managing feasibility constraints and trade-offs, as well as the potential of our proposed metrics in identifying and quantifying fairness issues.