Answer:
The Socs vs. the Greasers
In chapter three of The Outsiders, external conflict is present when the Socs find the Greasers walking with their girls, Cherry and Marcia.
Quote: "You know what soc is? White Trash with mastangs and madrus" Pg. 55
The conflict exists because they are two different groups of people.
Ponyboy vs. Darry
The main cause of this conflict, in my opinion, is the fact that Darry has been forced to serve as Ponyboy's parent or parents. ... Second, it makes Ponyboy unhappy because Darry is his brother acting as his parent. It is hard for Pony to accept the way Darry tries to protect him and make rules for him
Quote: "It was Darry." "He hit me. I don't know what happened, but I couldn't him hollering at me and hitting me too."
Darry and Ponyboy are very different. They love each other and all, but the changed since their parents died
Ponyboy vs. Himself
Ponyboy endures an internal struggle to find out who he is as a person outside of his role in his gang, the greasers
Quote: couldn't find anything within the text
Ponyboy has conflict with himself, he has experienced hardship in part because his parents died.
Hope this helps (^_^)