Cognitive Dissonance in Fight Club

mild spoilers

For those interested in the psychological aspects of the film, what would you say on Cognitive Dissonance in the film? I’m asking this for a research of a project in my university. We obviously know about the split personality disorder visible in the film, but does cognitive dissonance play a part in it? My project topic is about connecting cognitive dissonance with split personality. I wanted to explain it through this film.

Please let me know your elaborative opinions on this.