Since you want to design an API using the REST architectural style you need to think about your use cases to decide which concepts are important enough to expose as resources. Should you decide to expose the status of a group as a sub-resource you could give it the following URI and implement support for both GET and PUT methods:
/groups/api/groups/{group id}/status
The downside of this approach over PATCH for modification is that you will not be able to make changes to more than one property of a group atomically and transactionally. If transactional changes are important then use PATCH.
If you do decide to expose the status as a sub-resource of a group it should be a link in the representation of the group. For example if the agent gets group 123 and accepts XML the response body could contain:
<group id="123">
<status>Active</status>
<link rel="/linkrels/groups/status" uri="/groups/api/groups/123/status"/>
...
</group>
A hyperlink is needed to fulfill the hypermedia as the engine of application state condition of the REST architectural style.