  Weak lensing three-point statistics are powerful probes of the structure of
dark matter halos. We propose to use the correlation of the positions of
galaxies with the shapes of background galaxy pairs, known as the
halo-shear-shear correlation (HSSC), to measure the mean halo ellipticity and
the abundance of subhalos in a statistical manner. We run high-resolution
cosmological $N$-body simulations and use the outputs to measure the HSSC for
galaxy halos and cluster halos. Non-spherical halos cause a characteristic
azimuthal variation of the HSSC, and massive subhalos in the outer region near
the virial radius contribute to $\sim10\%$ of the HSSC amplitude. Using the
HSSC and its covariance estimated from our $N$-body simulations, we make
forecast for constraining the internal structure of dark matter halos with
future galaxy surveys. With 1000 galaxy groups with mass greater than
$10^{13.5}\, h^{-1}M_{\odot}$, the average halo ellipticity can be measured
with an accuracy of ten percent. A spherical, smooth mass distribution can be
ruled out at a $\sim5\sigma$ significance level. The existence of subhalos
whose masses are in 1-10 percent of the main halo mass can be detected with
$\sim10^4$ galaxies/clusters. We conclude that the HSSC provides valuable
information on the structure of dark halos and hence on the nature of dark
matter.
