Your definition is incomplete, you must assign priorities.
For instance, you want each group to have the same number of items and you only want max 6 groups. If you only have 1 group containing all items, that would satisfy the requirements, but you probably don't want that :-)
You also don't specify if you want to allow the same number to be in more than one group, though it looks like you don't, from your example.
Update: you also in other words: you don't specify how you want to score the returned groups. For instance, why don't you prefer (pseudocode):
[
[1 1 1 2 3],
[4 4 4 5 5],
[6 6 6 7 7],
[8 8 8]
]
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