Divide swingers' group? (6)

I believe the answer is:

bisect

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'divide' is the definition.
(I've seen this in another clue)

'swingers' group?' is the wordplay.
'swingers'' becomes 'bi' (I can't explain this - if you can you should give a lot more credence to this answer).
'group?' becomes 'sect' (I've seen this in other clues).
'bi'+'sect'='BISECT'

Can you help me to learn more?

(Other definitions for bisect that I've seen before include "cross" , "fork" , "Divide into two equal parts" , "Halve (angle)" , "Cut or divide in two" .)

I've seen this clue in The Independent.

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