To delete a family group, all members and administrators need to leave the group. After everyone leaves or is removed from a group, including its last administrator, the group is no longer available for use, even to the person who created it. Former group members can either create or join a different group.
If you created a group and accidentally removed yourself and all members from it, contact FamilySearch. A system administrator can reinstate the group.
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How do I leave a family group?
How do I remove someone from a family group?