Be careful, these groups are only indicative. The transmission, vertical or horizontal, is indicated as the transmission mode the most usual for the bacterium.

Mutualistic intracellular bacteria with vertical transmission
Parasitic intracellular bacteria with vertical transmission
Parasitic intracellular bacteria with horizontal transmission
Parasitic extracellular bacteria with horizontal transmission
Mutualistic extracellular bacteria with horizontal transmission
Commensalist bacteria with horizontal transmission
Free bacteria