The journeys of our protagonists take them into a dome dominated by a military society. All the women died centuries ago, while the men have continued onward through cloning. It's an all male society, where the governor wins his position through mortal combat. If this doesn't sound bad enough, all strangers are immediately suspect as mutants. To make things awkward and slimy, Rachael is a woman, and is immediately declared a goddess for the political advantage of the governor. He plans to marry her to seal his position against all rivals. Rachel's companions fight free, taking sanctuary with the priests, who actually know something about the ark and its purpose. Deciding to end the charade, one of protagonists fights the governor in moral combat, winning the fight, but leaving the governor alive. They manage to escape.
The plot of this particular story seems straight forward at first, but that's only because I explained them well. As played out in the show, the plot resembles a demolition derby, where the various points crash into each other until all the plot points are fully broken, and even the sole surviving plot point is barely operational.
You'll recognize some familiar faces in this episode. Barry Morse played the chief priest. John Colicos played the governor. Not surprisingly, both went on to playing similarly toned SF roles in the future.
This particular episode took me three sittings to get through, the overall episode having the engagement of a minefield.