How to embed a Google Group in a Google Site

1. Open your Google Site and navigate to the page where you want to add the group.

2. Click the "Insert" tab on the right-side panel.

3. Choose the "Embed" option and then click the "Embed URL" tab.

4. Find your group's URL by going to groups.google.com and selecting your group.

5. Paste the group's URL into the text field in Google Sites and click "Insert".

6. Resize and position the embedded group on your site as desired.

7. Publish your Google Site to make the changes live. 

Padlet can support a kind of threaded discussion (you can comment and reply to posts), but it is not equivalent to a full-featured discussion forum with multi-level nested threads. If your need is simply: post → comment → maybe reply, then it works. If you need robust thread hierarchies, sub-forums, deep nesting of replies, then you might need a more dedicated forum platform.