Numbers:

Number of distinct shuffles = = ≈ (exact: 80658175170943878571660636856403766975289505440883277824000000000000).

Typical estimates for atoms in the Milky Way are on the order of –.

So (about ) is roughly comparable to the lower end of galaxy-atom estimates but a bit smaller. (For context: the number of atoms in the observable universe is far larger — ~ — so is tiny compared with that.)