On the number of non isomorphic subspaces of a Banach space
  If a Banach space has an unconditional basis it either contains a continuum of non isomorphic subspaces or is isomorphic to its square and hyperplanes and satisfies other regularity properties. An HI Banach space contains a continuum of non isomorphic subspaces. 
Valentin Ferenczi & Christian Rosendal