We study the orbit of
R
^
\widehat {\mathbb {R}}
under the Möbius action of the Bianchi group
P
S
L
2
(
O
K
)
\rm {PSL}_2(\mathcal {O}_K)
on
C
^
\widehat {\mathbb {C}}
, where
O
K
\mathcal {O}_K
is the ring of integers of an imaginary quadratic field
K
K
. The orbit
S
K
{\mathcal {S}}_K
, called a Schmidt arrangement, is a geometric realisation, as an intricate circle packing, of the arithmetic of
K
K
. We give a simple geometric characterisation of certain subsets of
S
K
{\mathcal {S}}_K
generalizing Apollonian circle packings, and show that
S
K
{\mathcal {S}}_K
, considered with orientations, is a disjoint union of all primitive integral such
K
K
-Apollonian packings. These packings are described by a new class of thin groups of arithmetic interest called
K
K
-Apollonian groups. We make a conjecture on the curvatures of these packings, generalizing the local-to-global conjecture for Apollonian circle packings.