Bergey's 4 Divisions of Bacteria

Gracilicutes
Gracilicutes (gracilis=slender, and cutis=skin) have a cell wall that is consistent with being gram negative even though they do not necessarily stain gram negative.

Examples of gracilicutes include E. coli, Klebsiella Pneumoniae, Neisseria, Rickettsia, Chlamydia, Borrelia, Treponema pallidum.

Firmicutes
Firmicutes (firmus=strong, and cutis=skin) have mostly a gram positive cell wall structure.

Examples include Bacillus, Staphylococcus, Streptococcus, Clostridium, Mycobacterium, Corynebacterium diphteriae.

Tenericutes
Tenericutes (soft skin) have no cell wall. A notable example is mycoplasma s.

Mendosicutes
Mendosicutes (faulty skin) have no murein in cell walls, and are also known as archaea. These can stain both gram positive or negative, since archaea have a lot of variety. Defective cell wall with unusual cell wall composition.