Comets seem to be somewhat loose conglomerations of rock and ice. "Dirty snowballs" is a good description. Solar radiation absorption varies over the comet's surface (darker rock absorbs more than lighter ice) may cause uneven heating at a rapid pace, which may cause such fragmentation as we see in today's APOD. Another way to break up a comet is to let the Sun or Jupiter's tidal effects do the trick (remember comet Shoemaker-Levy 9?)
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