A Facebook Group can only be connected if your personal Facebook Profile is an administrator of that Group.
Sometimes, your Business Page may be set as the administrator instead of your Profile. In this case, you will need to promote yourself to an administrator.
Visit the Group on Facebook.com, then click "Members". You will see something like this:
As you can see, "My Example Brand" (a Page) is the administrator.
Find yourself in the "All Members" list, and click the [...] button.
Click "Make Admin" to promote yourself to an administrator. You should now be able to connect the Group correctly.