(0) Each child manages its visibility independent of the parent group. Toggling the parent's visibility should not change the child's visibility. In a table of contents, the children might be displayed with check boxes to change their visibility.
(1) Each child inherits the visibility of its parent group. The visibility of children should match that of the parent. In a table of contents, the children might be displayed with checkboxes whose values are bound to the parent or disabled. Alternatively, the children may be hidden from the table of contents because they effectively operate as a single layer.
(2) Only one child is visible at a time. When one child is made visible, all other children should be made not visible. In a table of contents, the children should be displayed with radio buttons.