The major conflict in Sophocles' Antigone occurs between Creon, the king of Thebes, and his niece Antigone, who is the daughter of Oedipus and Jocasta, and also the sister of Ismene, Polyneices, and Eteocles.
When Antigone buries Polyneices, in violation of Creon's order, Creon sentences her to death. Throughout the play, Antigone is steadfast and unapologetic for her actions. As she prepares to meet her death, she wonders "What holy justice have I violated?" (Ian Johnston translation).
Creon also stubbornly clings to his view that the person who violates his decree should be put to death, even if that means killing his own niece (and also his future daughter-in-law). Near the end of the play, however, Creon changes his mind, persuaded by the prophet Teiresias.
Alas—it’s difficult. But I’ll give up.
I’ll not do what I’d set my heart upon.
It’s not right to fight against necessity.
Unfortunately for Creon, by the time he arrives at the place where Antigone has been entombed it is too late. Antigone has already hanged herself. So, whereas Creon is won over by Teiresias' arguments (which are couched in religious terms), he changes his mind too late and ultimately loses both his son and wife as well.