If you are using Visio 2010 or later, Container shapes might serve your needs better than group shapes. Group shapes are primarily designed for creating composite shapes, not so much for containing peer shapes. Container shapes do not hide or limit the functionality of their contained shapes. Container shapes can be configured to automatically resize to fit the shapes added to them. You can create custom container shapes if the out-of-the-box containers don't have the appearance you want.
A link that might help you get started: http://blogs.msdn.com/b/visio/archive/2009/08/25/organizing-diagrams-with-containers.aspx