  We present a study of the shapes, orientations, and alignments of Galactic
dark matter subhalos in the ``Via Lactea'' simulation of a Milky Way-size LCDM
host halo. Whereas isolated dark matter halos tend to be prolate, subhalos are
predominantly triaxial. Overall subhalos are more spherical than the host halo,
with minor to major and intermediate to major axis ratios of 0.68 and 0.83,
respectively. Like isolated halos, subhalos tend to be less spherical in their
central regions. The principal axis ratios are independent of subhalo mass,
when the shapes are measured within a physical scale like r_Vmax, the radius of
the peak of the circular velocity curve. Subhalos tend to be slightly more
spherical closer to the host halo center. The spatial distribution of the
subhalos traces the prolate shape of the host halo when they are selected by
the largest V_max they ever had, i.e. before they experienced strong tidal mass
loss. The subhalos' orientation is not random: the major axis tends to align
with the direction towards the host halo center. This alignment disappears for
halos beyond 3 r_200 and is more pronounced when the shapes are measured in the
outer regions of the subhalos. The radial alignment is preserved during a
subhalo's orbit and they become elongated during pericenter passage, indicating
that the alignment is likely caused by the host halo's tidal forces. These
tidal interactions with the host halo act to make subhalos rounder over time.
