Organic group - join private group on invatation

Hello all,

I need the following functionallity on my website by using the OG module:

Everyone on my site can make a group. But when you, as group creator, make a group. You need to have two choices: public group or private group. When public group is selected, everyone can join this group by selecting the join link on the groups directory and add group posts. When private is selected I want only give access to the users which I invited. So I invite some friends, those invited friends will be saved and get an invatation email. In this email is a link to the subscription page. They need to fill in their emailaddress (or something like that) and a check will be executed if they were invited. If so add user to subscribers, if not give message something like: "You're not invited for this group". I they are added to the subscribers the can add group posts.

Why can't I use the invite friend link as it is integrated now:
They get the following message

Hi. I'm a member of 'group' and I welcome you to join this group as well.
Please see the link and message below.

Group
Description
Join: http://www.website.nl/og/subscribe/groupid
Personal message

But everyone can now go to the link http://www.website.nl/og/subscribe/groupid. That's not a problem, but everyone can now subscribe and I only want the user which I invited to subscribe.

Can anyone help me to accomplish this functionallity