Part of a big organisation that is wooden (6)

I believe the answer is:

branch

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'part of a big organisation' is the definition.
(I've seen this before)

I can't explain the remainder of the clue.

(Other definitions for branch that I've seen before include "Lateral extension of river or railway" , "One shop of a chain" , "local office" , "Division of some larger organisation" , "part of a big organisation" .)

I've seen this clue in The Guardian.

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