  It is still an open question how the Solar system is structured beyond 100 au
from the Sun. Our understanding of this vast region remains very limited and
only recently we have become aware of the existence there of a group of
enigmatic bodies known as the extreme trans-Neptunian objects (ETNOs) that have
large orbits with perihelia beyond the orbit of Neptune. Four ETNOs -- Sedna,
Leleakuhonua, 2012 VP113, and 2013 SY99 -- have perihelia beyond 50 au. The
study of the ETNOs may provide much needed information on how this remote
region is organized. Here, we apply machine-learning techniques to the sample
of 40 known ETNOs to identify statistically significant clusters that may
signal the presence of true dynamical groupings and study the distribution of
the mutual nodal distances of the known ETNOs that measure how close two orbits
can get to each other. Machine-learning techniques show that the known ETNOs
may belong to four different populations. Results from the analysis of the
distribution of nodal distances show that 41 per cent of the known ETNOs have
at least one mutual nodal distance smaller than 1.45 au (1st percentile of the
distribution), perhaps hinting at past interactions. In this context, the
peculiar pair of ETNOs made of 505478 (2013 UT15) and 2016 SG58 has a mutual
ascending nodal distance of 1.35 au at 339 au from the Sun. In addition, the
known ETNOs exhibit a highly statistically significant asymmetry between the
distributions of object pairs with small ascending and descending nodal
distances that might be indicative of a response to external perturbations.
