Transmission electron microscopy, neutron diffraction, and synchrotron powder X-ray diffraction reveal a complex modulated structure on the doubly ordered perovskite NaLaCoWO6. Electron diffraction patterns as well as high-resolution transmission electron microscopy images clearly show a periodicity of 12a(p), where a(p) is the cell parameter of the generic perovskite, along either the [100](p) or [010](p) direction. Annular bright-field scanning transmission electron microscopy of slightly tilted samples shows that there is no chemical origin for the superstructure but that it is caused by geometric rearrangements. An atomic model of the superstructure is proposed on the basis of octahedral tilt twinning. At low temperature, NaLaCoWO6 undergoes a phase transition and the superstructure disappears. The compound takes on the more usual monoclinic P2(1) structure below the transition. Neutron powder diffraction reveals and electron diffraction confirms an unusually large temperature hysteresis, where the transition takes place at similar to 180 K on cooling and at similar to 320 K on heating. This hysteresis can be attributed to the necessity of rearranging the oxygen octahedra and the thus induced energy barrier for the transition.