NYSE Euronext’s control of U.S. stock trading is slipping away.

Two-hundred seventeen years after the New York Stock Exchange was founded under a Wall Street buttonwood tree, its modern-day parent executed a record low 30.2 percent of May’s trades, data compiled by Bloomberg show. That's down 2.8 points from February for the worst three months since June 2008. The beneficiary wasn’t Nasdaq OMX Group Inc., the Big Board’s main rival for 38 years. It was Direct Edge Holdings LLC and Bats Exchange Inc., which more than doubled their combined share since August to 22.8 percent.