Groups may only be deleted by the group creator/owner.
If you are the owner, navigate to Group Settings to complete the group deletion.
For Web:
Through Messenger:
1. Open Messenger (bottom right corner)
2. Select Groups
3. Select the group you wish to delete.
4. Click on the group settings icon.
5. Click the 3 dots in the top right corner and select Delete Group.
Through the Game:
1. Select Groups at the top of the screen.
2. Select the group you wish to delete.
3. Click on Group Settings
4. Click the 3 dots in the top right corner and select Delete Group.