As we have been a long time Google Workspace user (Google Apps for Work > G Suite), some groups have been created before the new Groups UI update.
As such, we realise some of our old Groups email do not appear under "All Groups", which were found within admin.google.com. groups.google.com/all-groups
Based on Google Support's help link, the answer wasn't exactly clear. https://support.google.com/a/answer/167429?hl=en https://support.google.com/a/users/answer/167427?visit_id=637728860005296389-3531870159&rd=1
We weren't able to find out how to save the right Group settings.
Maybe it took some time to take effect, but we changed the setting for "Who can see group" to "Organization members" and the group appeared in "All Groups".