Her mother was the Doctor's daughter. By the time of her elevation to the presidency, she had two grandchildren of her own, a boy and a girl. She was the great-great-great-great-niece of Ordinal-General Quences. When the Doctor decided to leave Gallifrey to travel the universe, he offered her the chance to come with him, but Susan declined due to her duties. (AUDIO: Auld Mortality) As such, the Doctor created a copy of Susan to travel with using his Possibility Generator so he would not be lonely.
She later ordered the Doctor to be captured as he was interfering with time after she had spent most of her term of office covering up what her grandfather was doing. Zeuro failed to take the Doctor back to Gallifrey. She had spent most of her reign covering up the Doctor's interference but when the Supreme Council found out she had to order his execution. She wanted to show the Doctor the effects of his meddling. After the matter was resolved, Susan switched places with her duplicate, having decided to travel with her grandfather, while the dying copy could take on her role on Gallifrey. (AUDIO: A Storm of Angels)
The Presidents are categorised by in-universe chronological order. Loose chronological order applies for the lists, but when in doubt (as with the temporal uncertainty of the Time Wars), list them in the order in which they were first depicted as Presidents in the real world.