  The double-perovskite A$_2$BB'O$_6$ with heavy transition metal ions on the
ordered B' sites is an important family of compounds to study the interplay
between electron correlation and spin-orbit coupling (SOC). Here we prepared
high-quality Sr$_2$MgReO$_6$ powder and single-crystal samples and performed
non-resonant and resonant synchrotron x-ray diffraction experiments to
investigate its magnetic ground state. By combining the magnetic susceptibility
and heat capacity measurements, we conclude that Sr$_2$MgReO$_6$ exhibits a
layered antiferromagnetic (AF) order at temperatures below $\sim$ 55 K with a
propagation vector q = (001), which contrasts the previously suspected spin
glass state. Our works clarify the magnetic order in Sr$_2$MgReO$_6$ and
demonstrate it as a candidate system to look for magnetic octupolar orders and
exotic spin dynamics.
