In a Group's Settings, you can turn off Notifications for that specific Group only. You can also configure messages from the Group to not show up in your Latest Posts stream.
- Go to the Group page.
- Click "Group Settings."
- Uncheck the box called "Send Email/SMS Updates" to disable email/sms notifications for the Group.
- Uncheck the box called "Show on Home Page" to remove Posts from this Group from your Home Page.