"enlarged" form and Aut(Spin(8))

Question

In https://en.wikipedia.org/wiki/SO(8)#Spin(8), it says that

"Sometimes Spin(8) appears naturally in an "enlarged" form, as the automorphism group of Spin(8), which breaks up as a semidirect product: Aut(Spin(8)) ≅ Spin (8) ⋊ S3."

Can someone explain what is the detailed main idea of this sentence?

Answer 1

I think the Wikipedia was incorrect, the corrected statement is

$$ Inn(Spin(n;\mathbb{R}))=Spin(n;\mathbb{R})/Z(Spin(n;\mathbb{R})) = SO(8;\mathbb{R})/\mathbb{Z}/2 $$

$$ Out(Spin(8;\mathbb{R}))=S_3 $$

$$ Aut(Spin(8;\mathbb{R}))=Inn(Spin(8;\mathbb{R})) \rtimes Out(Spin(8;\mathbb{R})) =(SO(8;\mathbb{R})/\mathbb{Z}/2 ) \rtimes S_3 $$ instead. someone should (I will) make correction to Wikipedia.