The following very provisional classification is copied from Wikipedia, and does not include many extinct taxa
Superclass
Crustacea
Class
Malacostraca Latreille, 1802
Subclass
Phyllocarida Packard, 1879
Order †Archaeostraca Claus 1888
Order †Hoplostraca Schram, 1973
Order Leptostraca Claus, 1880
Subclass
Hoplocarida Calman, 1904
Order †Aeschronectida Schram, 1969
Order †Archaeostomatopoda Schram, 1969
Order Stomatopoda Latreille, 1817
Subclass
Eumalacostraca Grobben, 1892
Superorder
Syncarida Packard, 1885
Order †Palaeocaridacea Brooks, 1979
Order Bathynellacea Chappuis, 1915
Order Anaspidacea Calman, 1904
Superorder
Peracarida Calman, 1904
Order
Pygocephalomorpha (shrimp-like basal eumalacastruca -
Carboniferous to
Permian)
Order Spelaeogriphacea Gordon, 1957
Order Thermosbaenacea Monod, 1927
Order Lophogastrida Sars, 1870
Order
Mysida Haworth, 1825 (= Mysidacea)
Order Mictacea Bowman et al., 1985
Order
Amphipoda Latreille, 1816 (sand hoppers and sand fleas. Tertiary to Recent.)
Order
Isopoda Latreille, 1817 (Terrestrial wood lice and pill bugs and their marine relatives;
Carboniferous - Recent.)
Order Tanaidacea Dana, 1849
Order Cumacea Krøyer, 1846
Superorder
Eucarida Calman, 1904
Order
Euphausiacea Dana, 1852
Order
Amphionidacea Williamson, 1973
Order
Decapoda Latreille, 1802 (see next unit)