Farnham's Freehold by Robert A. Heinlein

In this science fiction novel, a family survives a nuclear apocalypse by taking refuge in their fallout shelter, only to find themselves transported to a future where society has drastically changed. The protagonist, Hugh Farnham, and his family must navigate a world where racial roles are reversed, with white people subjugated by a technologically advanced black ruling class. The story explores themes of power, race, and survival as the characters grapple with their new reality and the moral dilemmas it presents.