The managers of a group may choose to create one or more subgroups in that group, as distinct from creating additional separate groups. With a few exceptions each subgroup of a group has the same features and controls as any other group, including the parent group.
It is those exceptions which matter when considering whether to make a subgroup to an existing group, or a separate group.
Related membership
One reason to use subgroups is that it can ease the management of the memberships.
Subgroup members must be members of the parent group
Direct Add
Members of the parent group may be directly added to subgroups
Open or Restricted subgroup membership
Subgroup membership can be open to parent group members, even when parent group membership is restricted.
Related addressing
One reason to use subgroups is that their email and web addresses have a common identity with those of the parent group.
Subdomain addressing
Explain the new format. Cite Mark's beta@ announcement (soon) or most recent post.
Legacy addressing
Explain the deprecated +subgroup addressing scheme.
Access Controls
Features in the subgroup can be made visible to parent group members, while still being hidden from the public.
Examples
Some example use cases for subgroups.
Moderators' group
A common desire is to support better communication among the management of a group. In Y!Groups and other email lists this is sometimes achieved by creating a separate group, whose membership is restricted to just the moderators and owners of the primary group.
This is a natural use case for a subgroup.
PTA group
Primary group is all PTA members, subgroups for board, teachers, school admin, and students.
The official Groups.io user documentation is in the Groups.io Help Center.