Group configurations shape social skills and learning outcomes by fostering student interaction and collaboration. Yet, the factors influencing group formation, social cohesion, and group stability have remained understudied in physics education. Here, we examine these factors in a cohort of 90 students from ninth and tenth grades at a private school in Chile. For a semester-long physics project, students were assigned to groups either through random allocation (control group) or given the autonomy to form their own groups (experimental group). Our findings indicate that the groups formed by choice developed stronger friendship bonds throughout the semester, while the groups formed randomly demonstrated greater levels of cooperation and more frequent changes in membership, suggesting weaker social cohesion. Additionally, tenth-grade students were more likely to stay in their original groups, possibly indicating increased social maturity. These findings emphasize the ongoing challenge in education of balancing student choice in group formation with the need for diverse group compositions that enhance learning. This study provides practical recommendations for physics teachers and researchers.