Why is AU small finance bank not in Private sector index but its present in Bank nifty

Why so ? AU Bank is private … right ? And its present in Bank nifty…

One of the reasons behind it might be related to AU Small Finance Bank not having any Futures and Options. As per the Methodology Document for Equity Indices (Page 28), a preference is given to companies which are available for trading in NSE’s F&O segment for the selection in Nifty Private Bank index -

In case of NIFTY IT, NIFTY Pharma and NIFTY Private Bank, a preference shall be given to companies that are available for trading in NSE’s Futures & Options segment at the time of final selection

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Thanks @Prayag