As I know, you can't specify a group as customer approval task (CAT) recipient. Actually there is one workaround using stakeholders but such use has not been planned by design I suppose.
I can understand the logic is very simple:
* Customers should use customer portal. CATs can be assigned just to customers as there is no customer groups in the system. Please take in account that officers can have a customer role as well. You can specify as many CAT recipients as you need. Then a separate approval task will be created for each recipient.
* Full client app is dedicated for IT staff. So you can assign officers and/or solution groups to Approval Task managed within the client. You can specify multiple recipients here also.
* If you need approvals from Officers(Groups) and Customers at the same time you can include two (or even more) different approval tasks (CAT and AT) in your workfllow.