# $p$-groups with isomorphic subgroup lattices

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).

• An example with $|P_i| = 3^5$ is given by Jack Schmidt here. – Mikko Korhonen Feb 11 at 13:06

## 1 Answer

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.