  Detection of higher order modes of gravitational waves in third-generation
(3G) ground-based detectors such as Cosmic Explorer and Einstein Telescope is
explored. Using the astrophysical population of binary black holes based on
events reported in the second gravitational wave catalog by Laser
Interferometer Gravitational Wave Observatory (LIGO) and Virgo (GWTC-2), in
conjunction with the Madau-Dickinson model for redshift evolution of the binary
black hole mergers, we assess the detectability of these higher order modes
using a network consisting of three third-generation detectors. We find that
the two subleading modes [(3,3) and (4,4)] can be detected in approximately 30%
of the population with a network signal-to-noise ratio of 3 or more, and for
nearly 10% of the sources, the five leading modes will be detectable. Besides,
a study concerning the effect of binary's mass ratio and its orbital
inclination with the observer's line-of-sight in detecting various modes is
presented. For a few selected events of the LIGO-Virgo catalog, we identify the
modes that would have been detected if a third-generation detector was
operational when these events were recorded. We also compute the detectability
of higher modes by Voyager and find that only $\sim$ 6 and 2% of the detectable
population will have an associated detection of (3,3) and (4,4) modes,
respectively. Observing these higher order modes in the 3G era would have a
huge impact on the science possible with these detectors ranging from
astrophysics and cosmology to testing strong-field gravity.
