All those Bravais flocks belong to the same lattice system for which the Bravais classes belong to the same (holohedral) geometric crystal class.
Lattice systems in two and three dimensions
In the two-dimensional space there exist four lattice systems:
In the three-dimensional space there exist seven lattice systems:
Note that the adjective trigonal refers to a crystal system, not to a lattice system. Rhombohedral crystals belong to the trigonal crystal system, but trigonal crystals may belong to the rhombohedral or to the hexagonal lattice system.
In previous editions of Volume A of the International Tables of Crystallography (before 2002), the lattice systems were called Bravais systems.
Section 8.2.8 in of International Tables of Crystallography, Volume A