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In Jomsocial 2x (2.6.3) you can show featured group in groups module. You can active it in Joomla backend: Jomsocial configuration/layout/Group List: Featured or Upcoming.
But in Jomsocial 3x that option does not exist. It was deleted. As I can show featured group in group module on Jomsocial 3x?
you can feature a group on the frontend.. First you must login as super admin, go to group page and you will see button on the right side of the group name.. just click on that button and your group will be feature :)
i have been asked or developer about this, and we're sorry because our developer change that module :) now every featured groups can be viewed on groups page like carousel slider :)
if you still want to create groups module like that, you must do a customization coding and this is beyond our support :) Sorry for that :)