Priority types can alert managers when a ticket is not assigned after a certain time period: Setting Priority Types and Alert Triggers
However, I believe we can alert the whole group via a workaround with Action Rules in the Processes section (Customize Process by Adding Action Rules): Criteria would be Tech is blank & Date Opened within the last (time period). The Action against would be sending an email to your group using the tags for more detailed information.
To add to this, here's an example:
The initial 'Not Assigned' alert will occur to all technicians in the Tech Group the ticket is assigned to.
You would only need to configure an Action Rule for tickets that may come in without a Tech Group (Request Types that don't automatically select Tech Group) or the other alerts if you are wanting the group rather than just the one technician to get the reminder.