"A great many" or "a great many of" holds essentially the same meaning, however no one would say "a great many of" in this sentence. "A great many of" is used in a different way.
For example:
A great many houses were knocked down by the earthquake. A great many of them were completely destroyed.
Do you understand the difference? "A great many" specifies the total amount while "a great many of" usually points to a certain amount within a group. If you wanted to say "a lot of houses were knocked down" that is also correct. Saying "a great many houses were knocked down" is a stronger way of saying it and would usually mean that a larger number were knocked down when compared to "a lot". "A great many" is also a way to stress what is most important about your sentence. If I said "a lot of houses were knocked down by the earthquake" then I could be stressing either the fact that houses were knocked down or that there was an earthquake. If I said "A great many houses were knocked down by the earthquake" then chances are I want to stress the fact that houses were knocked down instead of the fact that the earthquake occurred. Of course context is key to fully understanding how a sentence was meant by the author, but I would only write the sentence you've asked about if I really wanted people to understand the importance of how many houses were knocked down.