Brainbox loses one type (5)

I believe the answer is:

genus

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'one type' is the definition.
(I've seen this before)

I cannot understand how the rest of the clue works.

(Other definitions for genus that I've seen before include "Taxonomic class between family and species" , "Taxonomic grouping" , "Taxonomic group (biol.)" , "Part of the family" , "Category between family and species" .)

I've seen this clue in The Mirror.

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