Hi Jens,
Before moving on, I'd like to know which Office 365 subscription you are using, Office 365 small business (P plan) or Office 365 Enterprise (E plan) ?
Based on my testing, there is the Delivery Management when I click the DG details.
In this situation, I suggest you new a DG in Exchange Online ECP, and then click the details to check if there is the Delivery Management.
For more information about how to new a DG, please see:
http://help.outlook.com/en-us/140/ms.exch.ecp.newdistributiongroup.aspx
Thanks,
Keats Ge