The superconductor 2H-NbSe2 features vortices with a sixfold star shape when the magnetic field is applied perpendicular to the plane of the hexagonal crystal structure. This is due to the anisotropy in the quasi-two-dimensional Fermi surface tubes oriented along the c axis. But the properties of another, three-dimensional, pocket are unknown, in spite that it has a dominant contribution in many experiments. Here we measure vortices in tilted magnetic fields using a scanning tunneling microscope. We find patterns of stripes due to in-plane vortices and show how these change with the in-plane direction of the magnetic field. The shape of outgoing vortices is successfully compared with detailed calculations of vortex cores. Our data show that vortices exit at an angle with the surface and that the sixfold gap anisotropy is present over the whole Fermi surface.