Number of Abelian groups

From the Kronecker's decomposition theorem they correspond to the number of factorizations of 64 into prime powers. They are only eleven: $2^6 \\ 2^4\cdot 4 \\ 2^2\cdot 4^2 \\ 4^3 \\ 2^3\cdot 8\\ 2\cdot 4\cdot 8\\8^2\\ 2^2\cdot 16\\4\cdot 16\\ 2\cdot 32\\64$ In the list, for example $2^2\cdot 16$ , represents the groups isomorphic to $\mathbb{Z}_2 \times\mathbb{Z}_2 \times \mathbb{Z}_{16}$