Antiferromagnetic (AFM) materials possess a well-recognized potential for ultrafast data processing thanks to their intrinsic ultrafast spin dynamics, absence of stray fields, and large spin transport effects. The very same properties, however, make their manipulation difficult, requiring frequencies in THz range and magnetic fields of tens of Teslas. Switching of AFM order implies going into the nonlinear regime, a largely unexplored territory. Here we use THz light from a free electron laser to drive antiferromagnetic NiO into a highly nonlinear regime and steer it out of nonlinearity with magnetic field from a 33-Tesla Bitter magnet. This demonstration of large-amplitude dynamics represents a crucial step towards ultrafast resonant switching of AFM order.