What "Line" are the people in front of the palace descended from in Oedipus Rex?

At the beginning of Oedipus Rex, the Priest makes a reference to the people being from the house of Cadmus. In Greek history, Cadmus is the first hero of Greece and the founder and first ruler of Thebes. Cadmus is an important figure, being one who killed monsters such as the dragon to protect the people. It is also thought that Cadmus is the one who introduced the Phoenician alphabet to the Greek people, which served as their literary foundation. After Cadmus's time, the descendants of Cadmus ruled in Thebes for generations, including Labdacus, the father of Laius, Laius himself, and then Laius' son by birth, Oedipus. So the ancestral foundation of the Theban people resides with Cadmus, and this common tie binds the people in the play.