This was a problem in the Scottish Book posed by Ulam. It was solved by
F. J. Freniche, The Number of Nonisomorphic Boolean subalgefbras of a Power Set, Proc. Amer. Math. Soc., 91 (1984) 199-201.
the number of non isomorphic sub algebras is $2^{2^k}$ for any cardinal $k$
