Issue with assigning groups to users

Hello there,

I am having trouble with adding users to a specific group from the SharePoint Site

Currently, the above is the only 2 options I have displaying as to which 'Group' I can put the member under. I have, however, created a new group called 'Partners' which doesn't display from the list.

The permissions of that group are very similar to that of a Member however with slight alterations. 

How do I successfully get the Partner's option to appear in the box when I am adding 'Members'

Thanks in advance.