This group has two shells that open and close using two sets of muscles. The shells are bilaterally symmetrical; so each shell individually has symmetry, but are not symmetrical with each other.

Classes
            Orders

Lingulata- Inarticulated
(have phosphatic shells that lack an articulating hinge).

Lingulida
Acrotretida

Articulata- Articulated
(have calcitic shells that have a strong hinge mechanism).

Orthida
Strophomenida
Pentamerida
Rhynchonellida
Spiriferida
Atrypida
Terebratulida

For more information:

http://www.ucmp.berkeley.edu/brachiopoda/brachiopoda.html

http://palaeo.gly.bris.ac.uk/Palaeofiles/Fossilgroups/Inarticulate/index.html

http://www.palaeos.com/Invertebrates/Lophotrochozoa/Brachiopoda/E0A0E0Brachiopoda.htm