We observed the lenticular galaxy NGC 3998 with the Mitchell Integral-Field Spectrograph and extracted line-of-sight velocity distributions out to three half-light radii. We constructed collisionless orbit models in order to constrain NGC 3998's dark and visible structure, using kinematics from both the Mitchell and SAURON instruments. We find NGC 3998 to be almost axisymmetric, seen nearly face-on with a flattened intrinsic shape – i.e. a face-on fast rotator. We find an I-band mass-to-light ratio of $4.7_{-0.45}^{+0.32}$ in good agreement with previous spectral fitting results for this galaxy. Our best-fitting orbit model shows a both a bulge and a disc component, with a non-negligible counter-rotating component also evident. We find that relatively little dark matter is needed to model this galaxy, with an inferred dark mass fraction of just $(7.1^{+8.1}_{-7.1}){\rm per cent}$ within one half-light radius.