Ohio State Route 586 is a north-south highway in Northwestern Muskingum County. It runs from Ohio State Route 146, near Nashport, to the Muskingum/Licking County Line, near Black Run. OH St Rt 586 passes through the following towns in Muskingum County. Black Run OH St Rt 586 is not multi-plexed in Muskingum County. OH St Rt 586 intersects the following highways in Muskingum County. Ohio State Route 146, near Nashport. Ohio State Route 16, near Black Run.