Set of six split in two and fall asleep at noon (4-5)

I believe the answer is:

half-dozen

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'set of six' is the definition.
'half-dozen' can be an answer for 'six' (I've seen this in another clue). I'm not certain of the 'set of' bit.

I cannot understand how the rest of the clue works.

Can you help me to learn more?

I've seen this clue in The Irish Times.

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