Social media firm Snap Inc. (SNAP) is just a few days removed from its initial public offering (IPO), but there is already some potential controversy surrounding the stock's prospects to join some big-name exchange traded funds (ETFs).

The Council of Institutional Investors, which represents big institutional investors such as pension funds, has voiced concerns about Snap's voting structure, reports CNBC. Essentially, the publicly available shares of Snap have no voting rights, leaving almost all of the voting power in the hands of the company's founders and insiders.

The Council of Institutional Investors is reaching out to MSCI​ and S&P Dow Jones Indices regarding Snap's inclusion in indexes provided by those firms. The possibility that Snap could be left out of MSCI and S&P indexes could be a significant blow to the newly public company, which slipped below its offering price on Monday.

MSCI and S&P Dow Jones are the two largest providers of indexes for use by fund issuers, including ETF sponsors. At the end of January, ETFs using MSCI benchmarks had $511 billion in assets under management, according to the New York-based index provider.

MSCI is backtracking from plans to add Snap to its indexes, reports CNBC. As for S&P, that index provider did not plan to add Snap to its indexes right away and is taking time to study Snap's voting structure. If S&P opts not to include Snap in its indexes, that means the stock cannot join the S&P 500 and ETFs such as the SPDR S&P 500 ETF (SPY) and the iShares Core S&P 500 ETF (IVV). SPY is the world's largest ETF and most heavily traded security.

SPY and IVV have $245.1 billion and $98.8 billion in assets under management, respectively, meaning it would be a blow to Snap to miss out on inclusion in S&P benchmarks. In addition to ETFs, Snap would miss out on buying from active fund managers that benchmark to MSCI and S&P indexes if one or both of the index providers do not include the stock.

One ETF already holds shares of Snap, though at a scant percentage while others are expected to follow suit before the end of this month. However, none of those ETFs track MSCI or S&P indexes.