Kind of. The SEC is what is known as an 'independent agency' of the federal government. It exists apart from the executive branch of the U.S. government, though it has a lot in common with other executive agencies, like the DOJ.
One of the most important differences is that independent agencies like the SEC are more insulated from the President of the United States. The heads of other executive departments, who serve on the Cabinet, can be dismissed for no reason at all, while the head of the SEC can only be dismissed for cause. This gives the SEC a level of insulation from the prevailing political winds of the moment which, in theory, lets it regulate the markets with more certainty and less political pressure.