For every k≥3 there exist finite groups that are not k-factorizable; certain groups of order 4m lack 2-m-2 factorizations under Sylow conditions; only eight groups of order ≤100 fail the property for some k.
Gorenstein, Finite groups in which Sylow 2-subgroups are abelian and centralizers of involutions are solvable , Canad
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Factorizations of finite groups
For every k≥3 there exist finite groups that are not k-factorizable; certain groups of order 4m lack 2-m-2 factorizations under Sylow conditions; only eight groups of order ≤100 fail the property for some k.