When you separate yourself from a fringe group and make clear that you are not a part of it, this is an example of when you detach yourself from that group.
When a hood unzips from the jacket to which it is normally attached, this is an example of when the hood detaches.
When a military unit is sent on a secret mission, this is an example of when you detach the troops.
Detach a check from the checkbook; detach burs from one's coat.
Detach a calf from its mother; detached herself from the group.
To detach a ship from a fleet, or a company from a regiment.