What is the external conflict between Antigone and Ismene?

The external conflict between Antigone and Ismene is detailed at the very start of Antigone. It begins when Antigone details to Ismene that:

Creon buried our brother Eteocles / With military honors, gave him a soldier's funeral... / but Polyneices... / They say that Creon has sworn / No one shall burry him, no one shall mourn for him / But this body must lie in the fields, a sweet treasure / For carrion birds to find as they search for food. (Prologue, Antigone. 15-22)

Immediately, there is an opposition between tradition (being able to give a brother a proper burial) and the state (Creon, a person in political power, demanding Polyneices should not be buried). Antigone aggressively decides that she is going to bury her brother, which shocks Ismene, who proclaims, "Antigone, you are mad!"

Antigone rebels against the state, siding with family and tradition, whereas Ismene follows the rules of the state. This is the central external conflict between Ismene and Antigone, and it continues to be acted out through the rest of the play.