This issue is dedicated to register the work to make the backup of groups optional in Moodle 2.x (like MDL-18177) and also let the user select which groups will be backed up (like
MDL-25485) also allowing the users to select for which groups the members should be backed up too.
There is a branch with the code in Github on top of moodle/master : https://github.com/danielneis/moodle/tree/backup-groups
The patch can be found here: https://github.com/danielneis/moodle/compare/moodle-master...backup-groups
The only part that does not work right now is the groups members selection. For some reason the "set_source_sql" (backup/moodle2/backup_stepslib.php ,line 973) for members does not work as for groups.