<p>Identifying subgroup structure with varying parameters in the model is of great importance in practical applications, such as making treatment decisions, personalizing educational programs. To address this issue, we develop an approach based on concave fusion penalties to identify the group structure and estimate the parameters using rank regression, which can achieve robustness for heavy-tailed random errors while maintaining high efficiency under normal errors. Furthermore, we employ the local linear approximation and reformulate each iteration as a median regression problem to facilitate computation. Additionally, we demonstrate the oracle property of the estimator as the number of subgroups tends to infinity, whereas most existing robust methods only provide theoretical guarantees for a finite number of subgroups. Simulation studies demonstrate that the proposed method can effectively identify heterogeneous subgroup structures and estimate the parameter. We further demonstrate the effectiveness of our method through applications to real-world data, with a particular focus on the student performance dataset, highlighting its practical significance in addressing educational issues.</p>