If the organization is big enough, it might even be setup as two organizations, a 501(c)(3) that can accept tax-deductible contributions and a 501(c)(4) that can't.
Conservatives weren't the only organizations to setup under the section of the tax code that allows social-welfare groups to operate on a tax-free basis.
That unleashed a flood of contributions and spawned an array of new outside political organizations, most of which were setup to help elect Republicans.