I can imagine reasons for random grouping. For examples, existing invoices are randomly assigned to 6 different people for audition. Of course, something more to be said about the grouping, for example that the groups to be of about the same volume. Otherwise we can do this: first record goes to the first group, the second one goes to the second group, etc, the rest goest to the sixth group. I see no contradictions in this way of grouping with the initial question.
OK, I have anothier idea. Along with every record we select a number from 0 to 5. It can be, for example, the record number modulo 6. Then we just group by this field.