Physical Information: Based on a recessional velocity relative to the Cosmic Background Radiation of 8135 km/sec (and H₀ = 70 km/sec/Mpc), a straightforward calculation indicates that PGC 6240 is about 375 to 380 million light-years away, in reasonable agreement with redshift-independent distance estimates of about 340 to 360 million light-years. However, for objects at such distances we should take into account the expansion of the Universe during the time it took their light to reach us. Doing that shows that the galaxy was about 365 to 370 million light-years away at the time the light by which we see it was emitted, about 370 to 375 million years ago (the difference between the two numbers being due to the expansion of the intervening space during the light-travel time). Given that and its apparent size of about 0.7 by 0.6 arcmin for the central galaxy and brighter shells and about 1.35 by 1.3 arcmin for the outer shells (from the images below), the central galaxy is about 75 thousand light-years across, while the outer shells span about 145 thousand light-years.
"Companions" Note: PGC 6286 is a slightly nearer galaxy, and almost certainly not a physical companion of PGC 6240; however, there is enough information about it to make a separate entry appropriate. PGC 95365 is a more distant background galaxy, so it is also not a physical companion of PGC 6240; but in its case there is so little information available that I have not provided a link to its nonexistent entry.
Classification Note: This type of peculiar galaxy is difficult to classify, but the classification provided by Corwin seems reasonable to me, so other than adding "(shells)" to note what is most peculiar about it, I have used his suggestion.

Physical Information: Based on a recessional velocity relative to the Cosmic Background Radiation of 8975 km/sec (and H₀ = 70 km/sec/Mpc), a straightforward calculation indicates that PGC 6241 is about 415 to 420 million light-years away. However, for objects at such distances we should take into account the expansion of the Universe during the time it took their light to reach us. Doing that shows that the galaxy was about 400 to 405 million light-years away at the time the light by which we see it was emitted, about 410 million years ago (the difference between the two numbers being due to the expansion of the intervening space during the light-travel time). Given that and its apparent size of about 1.05 by 0.85 arcmin (from the images below), the galaxy is about 120 to 125 thousand light-years across.
Classification Note: PGC 6241 is used by The deVaucouleurs Atlas of Galaxies as an example of galaxy type (R₁R₂')SAB(rl)a (whence the type shown in the description line). The "B" in "AB" and the "l" in "rl" refer to a lens-like central structure resembling a bar, while the (R₁R₂') refers to the partial rings surrounding the central structure.

Physical Information: Based on a recessional velocity relative to the Cosmic Background Radiation of 8370 km/sec (and H₀ = 70 km/sec/Mpc), a straightforward calculation indicates that PGC 6286 is about 390 million light-years away. However, for objects at such distances we should take into account the expansion of the Universe during the time it took their light to reach us. Doing that shows that the galaxy was about 375 to 380 million light-years away at the time the light by which we see it was emitted, about 380 to 385 million years ago (the difference between the two numbers being due to the expansion of the intervening space during the light-travel time). Given that and its apparent size of about 1.2 by 0.9 arcmin (from the images below), the galaxy and its outer ring span about 130 thousand light-years.
Classification Note: LEDA and NED list this as a type Sc spiral; but since the outer "arms" look more like a distorted ring, I have added (R) and "pec", and altered "c" to (r?)c? to reflect the fact that the galaxy's core looks more like a type Sa galaxy with a central ring than anything else. Hopefully the question marks make it clear that an expert in galaxy classification might use a very different classification; but I feel certain that at least the "pec" is appropriate.

Physical Information: Based on a recessional velocity relative to the Cosmic Microwave Background radiation of only 215 km/sec (and H₀ = 70 km/sec/Mpc), PGC 6430 is about 10 million light-years away, in reasonable agreement with redshift-independent distance estimates of about 12 to 15 million light-years, especially given the fact that for such a nearby galaxy, peculiar velocities (random motions relative to neighboring galaxies) can substantially affect the Hubble Flow distance calculation. For that reason, it might be best to say that the galaxy's distance is 10 to 15 million light-years, instead of trying to decide which method of determining the distance is best. Given that and its apparent size of about 4.5 by 3.7 arcmin (from the images below), the galaxy is about 12 to 14 thousand light-years across if it is closer to 10 million light-years away, and about 18 to 20 thousand light-years across if it is nearer 15 million light-years' distance.
Note About Classification: The Spitzer Survey of Stellar Structure in Galaxies classifies this as type S/IAB(s)m, "S/I" meaning that because the galaxy is so loosely structured (as indicated by the "m") it is hard to tell whether it should be called a spiral galaxy or an irregular galaxy. LEDA and NED classify it as type IB, though NED gives a nod to its slightly curved shape by adding (s) to the classification. The type shown in the description line tries to reconcile the various classifications with the images shown below, with the addition of question marks (and an underlined "B" to indicate that it is more likely to be classified as barred than not) to indicate that any description of such a "messy" galaxy is bound to be disagreed with by one astronomer or another.