"He thinks he is somebody, but he is nobody."
Translation:Hij denkt dat hij iemand is, maar hij is niemand.
Because 'maar' is one of the few coordinating conjunctions, and these don't change the word order the way the subordinating conjunctions do. Here's the Duo link to the info: https://www.duolingo.com/skill/dn/Conjunctions-1%3A-Coordinating/tips-and-notes
I think Merrie's point is the salient one, but in any case the 'that' is implied in the English sentence. Grammatically, it begins the subordinate clause.
I think it's good it's not included, because it makes us (well, me, anyway) think about how to translate the sentence without it being there -- and to realise that I do have to include it in the Dutch sentence. It's these little differences that are important for us to all get our heads around if we want to learn to speak or write the language well.