This is one of the most interesting entries in this list, because it is one of the rarest occupied space groups at all. See also the paper by Urusov and Nadezhina about the frequency distribution of space groups in inorganic crystal chemistry:
Currently, the ICSD contains only 2 entries for this space group, namely:
Structural study on new ordered potassium-nickel fluoride-type oxides, strontium lanthanum magnesium manganese oxide and strontium lanthanum zinc manganese oxide
Byeon, S.H.; Kim, I.-S.; Itoh, M.; Nakamura, T.
Materials Research Bulletin (1993) 28, p597-p603
Structure and magnetic properties of oxygen pressure induced Sr1.5La0.5Cu0.5Ti0.5O4-d (0.0 <= d <= 0.25)
Byeon, S.H.; Chung, H.
Chemistry of Materials (2002) 14, p556-p561
Interestingly, both datasets were published by the same first author. And, interestingly, both structures were clearly wrongly assigned. A symmetry check of the given coordinate sets revealed that both structures exhibit P4/mmm symmetry.
So, it seems to be the case that there is indeed no single inorganic crystal and no mineral on the earth, which crystallizes in the space group P422.
What about the CCDC, the (metal-)organic world of crystals?
A search retrieves 9 hits. For 6 of them, no coordinates are available. From the three sets with coordinates, two were corrected by the CCDC staff members to be not P422 but P41212 instead.
Accordingly, one compound is left and with good chance it is the only crystal of the world, belonging to the space group P422:
tetrakis(µ2-acetato)-tetrakis(µ2- ferrocenecarboxylato)-tetra-platinum toluene solvate
Interaction of Ferrocene Moieties Across a Square Pt4 Unit: Synthesis, Characterization, and Electrochemical Properties of Carboxylate-Bridged Bimetallic Pt4Fen (n = 2,3, and 4) Complexes
Inorg.Chem. (2011), 50, 11384
3D rotatable model of [Pt4(µ-OCOCH3)4(µ-OCOC5H4FeCp)4]
There might be a second compound, which crystallizes in the space group P422. CrystalWorks (The Chemical Database Service at Daresbury) pointed to their entry:
CrystMet – 458169
M. V. Speka, V. Ya. Markiv, M. I. Zakharenko, N. M. Belyavina
Dopov. Nats. Akad. Nauk. Ukr., ? (2002), 89
Cell: 16.67, 16.67, 9.793, 90, 90, 90
Space Group: P422 (89)
Al – lightblue
Ga – purple
Y – orange
Checking the given coordinate set it can be conformed that this is indeed the symmetry of space group P422. Unfortunately, I have no access to the original paper for any additional information.
3D rotatable model of YAl2.6Ga0.4
The Y-Al-Ga ternary systems seem to realize very many and different structures, see for instance:
Isothermal section (400 °C) of the phase diagram of Y–Al–Ga ternary system in the region up to 33.3 at.% Y
M.V Speka, V.Ya Markiv, M.I Zakharenko, N.M Belyavina
Journal of Alloys and Compounds, 348, p138–145