TITLE: $p$-groups with isomorphic subgroup lattices
QUESTION [6 upvotes]: Given two non-abelian finite p-groups $P_1$ and $P_2$ of the same order that are not isomorphic.

Can $P_1$ and $P_2$ have isomorphic subgroup lattices?

(I'm not experienced with group theory, sorry in case this is not appropriate for MO).

REPLY [6 votes]: The answer is yes. You can find references at page 277 of the book
 Roland Schmidt: Subgroup lattices of groups, De Gruyter Expositions in Mathematics 14, Berlin: Walter de Gruyter. xv, 572 p. (1994). ZBL0843.20003.