Hello aberrebbi,
Please check out this link, which will guide you through how to manage Do Not Disturb settings, and may help: Use Do Not Disturb with Focus on your iPhone or iPad
Change your Do Not Disturb settings
If you don't want to be disturbed at a certain time, you can set a schedule and change other Do Not Disturb features to help you concentrate.
1. Go to Settings > Focus.
2. Tap Do Not Disturb.
3. You can select allowed or silenced notifications from people and apps, connect your Lock Screen or Home Screen, have this Focus turn on automatically, and add Focus filters.
As for your question about groups, can you let us know more about your goal, so we can better assist you? For example, are you referring to group contacts, group messages, or something else?
The above details will help us plan how to proceed.
Thank you.