Looking at the moons natural satellites in the solar system, the larger ones appear to fall in a few groups of sizes.
Eyeballing the above picture, there appear to be a bunch of big moons (the Galilean Jupiter moons, Titan, the Moon, Triton), then some medium sized moons around Saturn and Uranus, and then some smaller moons such as Enceladus and Miranda.
If I take a look at those moons on the list of solar system bodies ordered by size, there indeed appear to be significant gaps between those size groups. There is a gap between Triton (1353 km radus) and Titania (789 km radus) of 72%, and between Tethys (533 km radus) and Enceladus (252 km radius) of 111%. Including other solar system objects in the comparison does not change the gap between the big and medium moons much, Pluto and Eris join the 'large' group and Haumea joins the 'medium' group. The gap between medium and small moons is also not changed much if we include the other cis-Neptunian objects (Ceres joins the mediums, Pallas and Vesta the smalls). There is however a large number of transneptunian objects in this gap, although most of them don't have a well constrained size.
So is there an explanation for why these gaps in the size distribution of moons (and many other solar system objects) exist? Or is it just a random accident from the formation of the solar system?