  The ALICE Collaboration reports the first fully-corrected measurements of the
$N$-subjettiness observable for track-based jets in heavy-ion collisions. This
study is performed using data recorded in pp and Pb$-$Pb collisions at
centre-of-mass energies of $\sqrt{s} = 7$ TeV and $\sqrt{s_{\rm NN}} =
2.76$\,TeV, respectively. In particular the ratio of 2-subjettiness to
1-subjettiness, $\tau_{2}/\tau_{1}$, which is sensitive to the rate of
two-pronged jet substructure, is presented. Energy loss of jets traversing the
strongly interacting medium in heavy-ion collisions is expected to change the
rate of two-pronged substructure relative to vacuum. The results are presented
for jets with a resolution parameter of $R = 0.4$ and charged jet transverse
momentum of $40 \leq p_{\rm T,\rm jet} \leq 60$ GeV/$c$, which constitute a
larger jet resolution and lower jet transverse momentum interval than previous
measurements in heavy-ion collisions. This has been achieved by utilising a
semi-inclusive hadron-jet coincidence technique to suppress the larger jet
combinatorial background in this kinematic region. No significant modification
of the $\tau_{2}/\tau_{1}$ observable for track-based jets in Pb--Pb collisions
is observed relative to vacuum PYTHIA6 and PYTHIA8 references at the same
collision energy. The measurements of $\tau_{2}/\tau_{1}$, together with the
splitting aperture angle $\Delta R$, are also performed in pp collisions at
$\sqrt{s}=7$ TeV for inclusive jets. These results are compared with PYTHIA
calculations at $\sqrt{s}=7$ TeV, in order to validate the model as a vacuum
reference for the Pb$-$Pb centre-of-mass energy. The PYTHIA references for
$\tau_{2}/\tau_{1}$ are shifted to larger values compared to the measurement in
pp collisions. This hints at a reduction in the rate of two-pronged jets in
Pb--Pb collisions compared to pp collisions.
