In literary terms, a climax occurs when the reader knows who "wins" a conflict. In my opinion, the climax occurs in Scene VII, in which Antigone is discovered to have hanged herself. It is a grim win, but a win nonetheless. Creon is not the one who will decide her fate.
Antigone's suicide is one a series of tragedies, all resulting in Creon having lost his battles. His son Haemon has also died (by an accident of his own hand). Here is a summary of that scene:
A messenger enters and reports that Haemon has taken his own life. Eurydice, Creon's wife, comes from the palace to receive this information. She learns how Creon and his men first gave Polyneices an honorable burial, and how, when they came to Antigone's crypt, they found that she had hanged herself. Haemon, in grief, tried to stab his father and, failing this, impaled himself. Eurydice bears this news in silence, returning to the palace.
The conclusion of the play will bring all the tragedy home to Creon, who will eventually lose everything, including his wife. Eurydice, too, takes her own life.