Improvements to a system for enhancing the quality of group interaction, group activities, and group environments over computer networks. New features include the capacity for participants to form subgroups within a larger group, as well as to move about a virtual environment, interacting with other participants they come across in the environment as desired. Unique methods for creating and distributing structured group programs for use on the system, for playing computerized board games or card games on the system, and for building virtual social environments using the system are also disclosed. The system creates improved virtual environments for high-tech business meetings, on-line classrooms, conferences, group counseling sessions, internet trade shows, and private meeting places where family and friends can spend quality time together.