As far as I know:
(1) my friend's car - correct
(2) a car of my friend's - correct
(3) a car of my friend - incorrect
I'm curious about whether the correctness will remain the same if I add "one of":
(4) one of my friends' car - Is it still correct?
(5) a car of one of my friends' - Is it still correct?
(6) a car of one of my friends - Is it still incorrect?
(The question is about whether "one of" affects the genitive.)
an update:
I wrote "a car of my friend" is incorrect because:
forum.wordreference.com: the sentence "That's a car of John." is incorrect.
Therefore, I think, the sentence "That's a car of my friend." is incorrect too.
Therefore, I'm inferring, the phrase "a car of my friend" is an incorrect phrase.