Ember google user group

I want to embed a google group that I have created in a custom web page. I used the iframe code that google provides for embedding the group and it embeds fine. However, since this is a private group, then if you are not logged in, a message will display in the frame saying that this is a private group and you need to be logged in.

My question: Is there an easy way to only embed the group if you are logged in and have access to the group?

<iframe id="forum_embed"
  src="javascript:void(0)"
  scrolling="no"
  frameborder="0"
  width="900"
  height="700">
</iframe>
<script type="text/javascript">
  document.getElementById('forum_embed').src =
     '<group url here>'
     + '&showsearch=true&showpopout=true&showtabs=false'
     + '&parenturl=' + encodeURIComponent(window.location.href);
</script>`