Unfortunately Groups are being updated and embedding New Groups in sites will probably be deprecated. See Review feature availability & provide feedback

Instead of embedding I suggest that you provide a link to the group:

Use the Embed URL function on the Insert menu and enter your Group's URL

Here's a video from 'Steegle' showing you how to Embed Google Groups in New Google Sites.

For this Group:

  • Anyone can view content.
  • Anyone can join.
  • Anyone can post.
  • All posts are held for moderation.
  • Only members can view the list of members