An Azure subscription is a container for Azure resources. It is also a boundary for permissions to resources and for billing. You are charged monthly for all resources in a subscription. A single Azure tenant (Azure Active Directory) can contain multiple Azure subscriptions.
A resource group is a container that holds related resources for an Azure solution. The resource group can include all the resources for the solution, or only those resources that you want to manage as a group.
To enable each department administrator to manage the Azure resources used by that department, you will need to create a separate subscription per department. You can then assign each department administrator as an administrator for the subscription to enable them to manage all resources in that subscription.
Reference:
https://docs.microsoft.com/en-us/azure/cost-management-billing/manage/create-subscription
https://docs.microsoft.com/en-us/azure/cost-management-billing/manage/add-change- subscription-administrator