To make sure users outside of your organization are able to send email notifications to the group, you'll need to correctly configure access settings for that group. When adding recipients to email notifications, you have the option to add groups.
View or edit group access settings for email notifications If an alert center alert is available for the rule, the Alerts column shows On. (For rules that don't generate an alert center alert, a dash appears in the Alerts column.).The Actions column shows Send notification.On the Rule details page, click Rules at top left to return to the Rules page.To make sure users outside of your organization are able to send email notifications to the group, you'll need to correctly configure access settings for that group. For instructions, see View or edit group access settings for email notifications in the section below. When adding recipients to email notifications, you have the option to add groups. (For rules that dont generate an alert center alert, a dash appears in the Alerts column.) View or edit group access settings for email notifications. Important: When adding recipients to email notifications, you have the option to add groups. If an alert center alert is available for the rule, the Alerts column shows On. In Send email notifications, you have the option to select All super administrators as well as click Add email recipients to add multiple recipients from the list of users in your domain.If you turn off an alert, email notifications are not sent. If the Alerts option is present, be sure the alert is turned On, and choose a default severity level.Click a rule to open the Rule details page.For all of them, you can set up email notifications. For some of these events, you can turn on alerts, which means they will appear in the alert center. The Rules page lists rules for trackable security events such as a suspicious login, a compromised device, a leaked password, or a new user added. On the Admin console Home page, go to Rules.