GR translation: an order whose presence among the ordinary debris of waking

[Mike Jing]

P205.5-15   Brass-colored light seeps in from overhead. Murals line
the great room: pneumatic gods and goddesses, pastel swains and
shepherdesses, misty foliage, fluttering scarves. . .. Everywhere
curlicued gilt festoon-ery drips—from moldings, chandeliers, pillars,
window frames . . . scarred parquetry gleams under the skylight . . .
>From the ceiling, to within a few feet of the tabletops, hang long
chains, with hooks at the ends. What hangs from these hooks?
For a minute here, Slothrop, in his English uniform, is alone with the
paraphernalia of an order whose presence among the ordinary debris of
waking he has only lately begun to suspect.

What is the principal meaning of the word "order" here?  And what does
"the ordinary debris of waking" refer to?