7-3-4259. Discharge of employees. All persons subject to the civil service examination are subject to removal from office or employment by the council for misconduct or failure to perform their duties under rules that the council may adopt, and the chief of police, chief of the fire department, or any superintendent or lead supervisor in charge of municipal work may peremptorily suspend or discharge any subordinate then under that person's direction for neglect of duty or disobedience of orders but shall, within 24 hours, report the suspension or discharge and the reason for the suspension or discharge to the superintendent of the department. The superintendent shall affirm or revoke the discharge or suspension according to the facts. The employee or the officer discharging or suspending the employee may, within 5 days of the ruling, appeal to the council, which shall fully hear and determine the matter.