  A systematic analysis of resonant x-ray Bragg diffraction data for UPd$_3$,
with signal enhancement at the U M$_{IV}$ edge, including possible structural
phase-transitions leads to a new determination of the space groups of the
material in the phases between $T_0 = 7.8$ K and $T_{+1}$ = 6.9 K as P222$_1$
and between $T_{-1}$ = 6.7 K and $T_{2}$ = 4.4 K as space group P2$_1$. In
addition, the quadrupolar order-parameters, $<Q_{ab}>$, inferred from
diffraction data in the phase between $T_{-1}$ and $T_{2}$, are $<Q_{xz}>$ and
$<Q_{yz}>$ at the (103) Bragg reflection, and $<Q_{xy}>$ at the (104)
reflection.
