Are you sure you aren't? I think you need to talk to the IRS tax exempt group to help you classify your group correctly. There are a variety of 501c organizations. I think our (summer) community swim team is a 501(c)(4).
501(c)(1) — Corporations organized under acts of Congress such as Federal Credit Unions 501(c)(2) — Title holding corporations for exempt organizations 501(c)(3) — Various charitable, non-profit, religious, and educational organizations (see below) 501(c)(4) — Various not-for-profit organizations (see below) 501(c)(5) — Labor Unions and Agriculture 501(c)(6) — Business league and chamber of commerce organizations (see below) 501(c)(7) — Recreational club organizations 501(c)(8) — Fraternal beneficiary societies 501(c)(9) — Voluntary Employee Beneficiary Associations 501(c)(10) — Fraternal lodge societies 501(c)(11) — Teachers' retirement fund associations 501(c)(12) — Local Benevolent Life Ins Assoc. Mutual Irrigation and Telephone Cos. and like orgs 501(c)(13) — Cemetery companies 501(c)(14) — Credit unions 501(c)(15) — Mutual insurance companies 501(c)(16) — Corporations organized to finance crop operations 501(c)(17) — Employees' associations 501(c)(18) — Employee-funded pension trusts created before June 25, 1959 501(c)(19) — Veterans' organizations 501(c)(20) — Group legal services plan organizations 501(c)(21) — Black lung benefit trusts 501(c)(22) — Withdrawal liability payment fund 501(c)(23) — Veterans' organizations created before 1880 501(c)(25) — Title-holding corporations for qualified exempt organizations 501(c)(26) — State-sponsored high-risk health coverage organizations 501(c)(27) — State-sponsored workers' compensation reinsurance organizations 501(c)(28) — National railroad retirement investment trust