Make the invitation to the group visible to everyone, not just members
Membership is limited, in order to avoid spam.
But invitations to everyone, the "about" page should be visible to everyone in order to attract new members. Once people see what is available they can apply for membership and be accepted if they meet the requirements. It is important that the existence of the group is visible, for it to be able to grow.
It's up to the owner/moderator to make the group "listed in directory" and/or the archive "public" or not