Can someone please tell me what government agency oversees a COBRA plan

There's really no such thing as a "COBRA plan". COBRA allows you to remain part of your employer's group insurance program after termination of employment (if your employer is subject to COBRA).

The agency which oversees the notice requirements of COBRA is the U.S. Department of Labor's Pension and Welfare Benefits Administration. Most of the other provisions are overseen by the Internal Revenue Service.