Is there a way to give permission to a SharePoint Group to edit the membership of another SharePoint group ?
I guess you want the group members be able to edit permission of other group? If so, for default permission levels, you will need to grant full control.
When you edit permission level, you can find the site permission with named "Manager Permissions". It is the permission needed to assign permissions to users and groups.
For more information, please refer to this:https://docs.microsoft.com/en-us/sharepoint/sites/user-permissions-and-permission-levels