The board of trustees shall classify each member in one of the following groups:

(1) General employees of the State and counties, including administrative, clerical, professional, and technical workers, mechanics, laborers, and all others not otherwise classified;
(2) Teachers, including all teachers regularly engaged in public education whose salaries are wholly or partly paid by the State, and faculty members and instructors of the University of Hawaii; or
(3) Police officers in the employ of the counties and firefighters in the employ of the State or of the counties,

or in any other group that may be recommended by the actuary on the basis of service and mortality experience and approved by the board, to cover any part of any group or groups previously created or any additional class of employees.