Witt (1941) mentions that he found more than 10 such lattices, but gives no further details.
The Dynkin diagrams associated with a Niemeier lattice have rank either 0 or 24, and all of their components have the same Coxeter number.
The complete list of Niemeier lattices is given in the following table.
Each point represents one of the 24 Niemeier lattices, and the lines joining them represent the 24 dimensional odd unimodular lattices with no norm 1 vectors.
The red index number in the node indicates the row of the associated table above.
Some of the Niemeier lattices are related to sporadic simple groups.