Who are the owners of big public corporations? If you have an IRA, maybe you're an owner of Facebook as part of an index fund. But do you really own the fund?

Who are the owners of big public corporations? If you have an IRA, maybe you're an owner of Facebook as part of an index fund. But do you really own the fund? Or does the broker/bank own it for you? Does the index fund manager own the stock, such as Vanguard or Blackrock? Or is it really owned by The Depository Trust & Clearing Corporation for the fund?