One of the most complete Visio discussions is here:
https://docs.microsoft.com/en-us/previous-versions/office/developer/office-xp/aa200971(v%3doffice.10). In particular application here: chapter 6 and it's section on groups.
There's nothing really special about a sub-shape, other than, by definition, it is part of a group. The group is the top-level shape. A group, can contain both individual shapes, i.e., sub-shapes, and it can contain other groups.
For example, you make a bunch of animal shapes, dogs, cats, etc. Each animal shape could be a group of shapes. The dog group, might have individual shape for legs, tail, body, head, etc. Then, these pet shapes might be part of a group called, MyPets. Certain shape data, might be entered at the group level, e.g., pet names, or pet color. This information could then be pushed down to the appropriate animal group. So, you might have a brown dog, a yellow canary, and a black cat.
Check out the link though. Hope this gives a better idea of what a group is, and how it can be configured.
Wapperdude,
PS: your pet snake might only be a sub-shape, and not a group...unless, it's a rattle snake, then, the snake might be a group, which includes the main body, and the rattles.