Upon application of any club or organization having 10 or more members who are citizens of this state, or upon the application of 10 or more citizens of this state, and the payment of a registration fee of $5.00, the department, pursuant to part 13, may issue a permit authorizing the establishment and maintenance by the club, organization, or citizens on land owned by them, or over which they have legal control, of a special dog training area where dogs may be trained at any time during the year. A dog training area shall not be less than 40 acres or more than 240 acres, and permits shall not be issued for more than 6 special dog training areas in any 1 county. In counties having a population of 100,000 or more, the department may issue additional permits as the department considers to be in the public interest.