When you receive an invitation to join a Group, you automatically get an alert which warns you that some Groups prevent members from having private Projects. If you recall seeing this warning, then that is the reason to why your private Projects are no longer visible. If you didn't receive the invitation, it could also be because your Group Admin has changed the Group settings to prevent Group members from having private Projects after you joined the group. In that case, your private Project folder gets removed from your Projects page. To access your private Projects once more, please contact your Group Admin and request temporarily changing the settings to allow private projects.
In case private Projects are prevented already by Group Setting and one wants to keep them, then one cannot join the respective Group, and moving private Projects to the Group Folder is not possible. It is possible, however, to remove the user with private Project from a Group, change the settings to prevent private projects, and re-invite the user.