The state board of land commissioners may cause any portion of state lands to be laid out in subdivisions of less area than the legal subdivisions of the United States survey, upon showing to the satisfaction of the board that said subdivisions will be more salable or will sell at a better price than when undivided or that public convenience will be served thereby. A plat of any such subdivisions shall be filed in the office of the recorder of the county where said lands are situated. The board may sell such subdivisions from time to time, at public auction, in such quantities and on such terms as shall enable the state to realize the best prices therefor.