This book is really good for learning about basic neuroscience if you are a layman with HS math and physics/chemistry but it says that neanderthals were humans.
I don't know enough about the topic to argue but the wikipedia page for neanderthal links me to three other pages:
Human - homo sapiens
Modern Human - homo sapiens
Ancient human - neanderthals, denisovans etc
All of this is fine but carefully reading these and googling doesn't answer this followup question:
What is the boundary between non-human great ape and ancient human? Is it paranthropus? Australopiths?