Is Beatrice a reliable narrator? Does she always tell the truth? Does she always know the truth? Is she naive or does she sometimes miss things that are obvious to you?
Does the way the city is organized by faction make sense to you? Does it make sense that, for example, the Dauntless are the guards of the city? Does that mean that you don't have to be smart or friendly to be an effective guard—only brave? In your day-to-day life, can you break down everyone's job into one of the five factions?
What about the factionless? Do they have a role in this city? Some people fail out of Dauntless's initiation, but do the other factions produce some factionless folks? Are there any people in the real world who seem to fit the "factionless" description?
Why do you think this setting is limited to one particular city? Would it change the story much if the United States were still a country? (And how do you feel about it being Chicago?)
Is this setting a dystopia, a utopia, or just the future? Does this future society seem possible? Or do you read this book as a warning ("don't let things become like this")? If this is a dystopia, is there anything good in it that we should have in our world?
There are a lot of things that don't get explained in this book—like how the factions formed or why Lake Michigan is a swamp or what Dauntless is protecting the city from. How do you feel about those issues not being explained? Did it make you curious? Did it make you believe the world more or less? Did it seem like an attempt to get you to buy the sequel?
What is the most important relationship that Tris has in this book? Is it Tris and her family? Or Tris and her faction? Or Tris and her friends? Or Tris and her boyfriend Four? Do these relationships help her to figure out who she is? Are any of these dangerous or problematic for Tris?
What do you think about Tris and Four starting a relationship? Could you tell that Four liked her before Tris figures it out? Do you have a clear idea about why they like each other? Does it have anything to do with their shared history (being born into Abnegation families but joining Dauntless)? Or is there something else?
What do you think about the enemies in this book, like Peter, Molly, and Drew, the bullies in Tris's class? How does the book show us that they are the enemies? Are they "pure evil" (9.14) or something else (misguided, selfish, dumb, sleepy)? What about the older enemies, like Eric or Jeanine? Do all of Tris's enemies share some qualities?
What do you think about Tris's thoughts about herself? She says "I am ___" quite a bit in the book. Does her self-description always match up with reality? Does that help you to understand what she's going through?
Compare and contrast time: choose one element of Divergent and compare it to a similar element in a different book. For instance, take the training where Tris and her friends have to beat up each other and compare it to fighting in the arena from The Hunger Games or fighting in battle school from Ender's Game. What are the differences and how do those differences make you feel about these books? For another example, how does this dystopian city compare to the city of Westerfeld's Uglies?
Do the chapters end in cliffhangers where you have to read the next chapter to find out the answer to some question or twist? Or does each chapter finish telling a part of the whole story? How does this long book keep the reader reading from chapter to chapter?
How did you feel about the supplementary material in the book, like the factions' manifestos? Did those help you to understand this world? Did you wish those manifestos were worked into the plot of the book somehow?