Observations of comets in Sun-grazing orbits that survive solar insolation long enough to penetrate into the Sun's inner corona provide information on the solar atmosphere and magnetic field as well as on the makeup of the comet. On 6 July 2011, the Solar Dynamics Observatory (SDO) observed the demise of comet C/2011 N3 (SOHO) within the low solar corona in five wavelength bands in the extreme ultraviolet (EUV). The comet penetrated to within 0.146 solar radius (similar to 100,000 kilometers) of the solar surface before its EUV signal disappeared. Before that, material released into the coma-at first seen in absorption-formed a variable EUV-bright tail. During the final 10 minutes of observation by SDO's Atmospheric Imaging Assembly, similar to 6 x 10(8) to 6 x 10(10) grams of total mass was lost (corresponding to an effective nucleus diameter of similar to 10 to 50 meters), as estimated from the tail's deceleration due to interaction with the surrounding coronal material; the EUV absorption by the comet and the brightness of the tail suggest that the mass was at the high end of this range. These observations provide evidence that the nucleus had broken up into a family of fragments, resulting in accelerated sublimation in the Sun's intense radiation field.