'That' isn't the subject or object, and it's not a relative pronoun. It's a conjunction.
Do you understand the following sentences:
"How fat was she? She was so fat that she had to go on a diet." Era cosė grasso che ...
"How hungry was he? He was so hungry that he ate four hamburgers."
The construction is: ... so X that Y ... "cosė Y che Y"
"The paper was so revolutionary ... that it had to be smuggled back to Germany."