Ventsharm can you provide more details about which extension(s) you are using and what you are trying to achieve?
The native Flarum feature called "Group" is only a mechanism to manage user permissions, aka a Role.
If you want members of that Group to have a private area to create discussions, you can create a Tag and use the Permissions tab in the admin panel to configure it so only a specific Group can see and/or post inside that tag.
Extensions exist to manage how a group is obtained/joined. There are also extensions that modify how a tag visibility works, to create for example a private support area.
