The paper studies statistical dependences in 4 groups of near-solar comets. It is shown that the perihelia of the of the Kreutz-family comets are clustered around two planes («great circles» of the celestial sphere). Numerical data on the observed bifurcation of the perihelion distribution are provided. One of the planes practically coincides with the plane obtained by averaging the orbital parameters and i. The second plane with parameters = 77.7°, = 266.1° has an inclination of about 64°. The distant nodes of cometary orbits relative to this plane are clustered at a distance of about 2 a.u. On this basis, one of the authors for a certain period of time defends the hypothesis of the origin of the group through the impact of a large comet with a meteoroid stream. The article examines some counterarguments expressed regarding this hypothesis. Using a concrete case, it is shown that the assumptions about the concentration of comet perihelia near one point and along two circles of the celestial sphere are quite compatible. The distribution of orbital inclinations relative to this plane is analyzed and a sharp maximum near 90° is noted. This maximum, in all probability, indicates that the impacts of meteoroid bodies causing defragmentation of the parent body were of a lateral nature. New confirmations of the already existing hypothesis about the presence of another group of «sungrazers» have been found. It is assumed that the correlation dependence between the values of the arguments of perihelion and ascending nodes of cometary orbits is of an evolutionary nature and is related to the process of group formation. New regularities concerning the Meyer, Kracht, and Marsden groups are introduced. In particular we calculated the planes near which the cometary perihelia of these groups are concentrated. The example of the Meyer group illustrates the bifurcation of perihelia.