The Pyramid of Control
The main alien spaceship called the Tetrad obviously represents the pyramid of control, the Illumanti power structure, centered in Rome. Note throughout the film the Tetrad pyramid spaceship, is shown upside-down to the way a pyramid is normally.
This is just like satanist turning the cross of religion upside-down to disrespect it, so the inversion of the pyramid is showing disrespect to the Illuminati power structure. Also inverting the pyramid now places the people who were at the bottom of the pyramid above those who used to control them, showing the gaining of power by the awakened people.
