There shall be a Department of Finance, a Department of Law, a Department of Safety, and a Department of Service, and such other departments as may be established by the administrative code. Each department shall be headed by a full-time or part-time director, appointed by the Mayor. Such director shall have supervision and control over the department personnel of his department under the immediate direction of the Administrative Assistant to the Mayor. Two or more departments may be headed by the same person. The Administrative Assistant may serve as director of one or more departments, if so designated by the Mayor.