The Groups tab will display the list of groups that you are part of and all the open and closed groups that are in the spot but you are not a part of it yet. You will not find any private group in your group list as these are hidden groups.
To join a feed group, follow the steps below:
Open group
1. Go to Groups and click on the + icon at the bottom
2. Click on Join Groups
3. Click on the Join button to become a part of the open group
You will now have access to the group
Closed group
1. Go to Groups and click on the + icon at the bottom
2. Click on Join Groups 
3. Click on the Request Join button to become a part of the closed group 
Once the admin has approved your join request, you will have access to the closed group
Private group
The only way you can be a part of a private group is when the admin adds you to the group
When an admin adds to a group (open, closed, or private) you will be notified via an email, SMS, or app notification.