Summary: It is shown that the Hilbert space corresponding to all the quantum states of the Landau problem can be split in two different ways: as infinite direct sums of the finite- and infinite-dimensional representation subspaces of the Lie algebras \(su\)(2) and \(su\)(1,1) with finite- and infinite-fold degeneracies, respectively. For each of the Hilbert representation subspaces of the Lie algebra \(su\)(1,1), we construct a suitable linear combination of its bases as the Barut-Girardello coherent states.