There is a construct to allow randomizing the display of questions with "groups" that you can define -- it gives the flexibility of randomizing questions without being limited to physical Question Groups, but you can also use it to randomize questions within a Question Group.
It will require you to edit each question within each group though.
You want to look for a field under the Advanced tab for each question. The field you are looking for is called "Randomization group name
You can enter any string in this field, and questions with the same value will be randomized together.
Then, if you want to randomize question order within each a set of Question Groups, all you need to do is the following (and repeat for each group):
For each question in Question Group 1, enter the string "Group1" into the field Randomization group name.
For each question in Question Group 2, enter the string "Group2" into the field Randomization group name.
Of course, if you wanted questions in a Question Group to not be displayed in a random order, then you'd leave the field Randomization group name blank.
You can also use this feature to span across Question Groups.
We always suggest you try it with one question group first, to make sure you get the results you expect.