To clear confusion I'll write how Draco got his detention with Hagrid.
"Here's what you need to add" Professor Snape says grabbing his own quill and writing a side note. "How does the cure for boils cause boils?" Draco asks his final question about the class essay. "That's an easy answer, Mr. Malfoy, adding porcupine quills to the potion still on the fire, causes it to burn and create boils" Professor Snape answers. "Student out of bed! Snivellus help us find them" Potter yelled barging into the Potions Room.
"Why is there a student in here?" he questions with an irritated face. "I was helping him with his essay, Potter. Why have you barged into my classroom?" Professor Snape snarls. "You should have informed us that it was a Slytherin, especially a Malfoy, sneaking out past curfew" Potter says with a smirk. "Mr. Malfoy, has permission to stay and ask questions about his work" Professor Snape informed as he guided Draco out.
"He'll be given a detention you know? He was out past curfew with a weak alibi" Professor Potter said. "I'm his alibi, Potter. Now please go find the real idiot out past curfew" Professor Snape irritation lacing his voice. "Ah James, have you found the student?" questions the joyful Dumbledore. "Yes, Mr. Malfoy was wondering the halls" Professor Potter answered.
"I was not! Professor Snape was helping with a potions essay and was about to walk me back to my common room" exclaimed Draco. "Now don't lie Mr. Malfoy, please tell us the real reason you were out of bed" Dumbledore said. "Mr. Malfoy is telling the truth. I can tell you two Gryffindors are walking in this hallway coming towards us" Professor Snape said pointing towards Zeke Potter and Ronald Weasley walking towards them with panicked looks.
"There are your goons out of bed. I'm going to drop Mr. Malfoy off into his dorm before heading to my own chambers" Professor Snape said pushing the tired Malfoy towards the dungeons. "Mr. Malfoy will have to attend detention with Mr. Weasley and Potter. He was out without permission" Dumbledore informed the two as they walked away.
"Alright Professor Dumbledore" Mr. Malfoy said quietly. As the two Slytherins made their way back to the common rooms they spoke quietly. "Attend the detention and inform me of what happens" Professor Snape said before he left towards his own room.
"Pureblood" Draco said entering his common room. He walked to his room, threw off his robe, before falling face first, falling asleep in his clothes.
I hope this clears up any confusion of what happened with the detention. I made a mistake not clearing up how the detention was actually given. The chapter was really rushed and it was not my finest work. So keep reading and reviewing! Ja'ne~