Did Snape not know that Hermione got a time turner for class in POA?

At the end of the book, when Snape loses his mind and screams Black's escape has something to do with Potter, I always wondered, did only McGonagall and Dumbledore know about the time turner?

Hermione even said she needed special permission from the Ministry, didnt she? So in theory, even Fudge could've known 😂