  Antiferromagnetic (AF) order of U$_{2}$Pt$_{6}$Ga$_{15}$ with the ordering
temperature $T_{\rm N}$ = 26 K was investigated by resonant X-ray scattering
and neutron diffraction on single crystals. This compound possesses a unique
crystal structure in which uranium ions form honeycomb layers and then stacks
along the $c$-axis with slight offset, which gives rise to a stacking disorder.
The AF order can be described with the propagation vector of $q = (1/6, 1/6,
0)$ in the hexagonal notation. The ordered magnetic moments orient
perpendicular to the honeycomb layers, indicating a collinear spin structure
consistent with Ising-like anisotropy. The magnetic reflections are found to be
broadened along $c^*$ indicating that the stacking disorder results in
anisotropic correlation lengths. The semi-quantitative analysis of neutron
diffraction intensity, combined with group theory considerations based on the
crystallographic symmetry, suggests a zig-zag type magnetic structure for the
AF ground state, in which the AF coupling runs perpendicular to the stacking
offset, characterized as $q = (1, 0, 0)_{\rm orth}$. The realization of the
zig-zag magnetic structure implies the presence of frustrating intralayer
exchange interactions involving both ferromagnetic (FM) first-neighbor and AF
second and third-neighbor interactions in this compound.
