Cost Center Groups are used for creating standard hierarchy in an organization, Cost Centers will be assigned to the cost center groups.
eg: If there is a cost center called Machine Hours the same will be assigned to concerned hierarchy which is the cost center group it may be a case specific.
Cost Element Group: Cost Element group is generally used for bringing all the cost elements which are similar. These may be used for further allocation or distribution.
eg: If u want to check personal costs at a time, then u can select the personal cost group so that all the personal elements in the group will be displayed.