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).
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4$\begingroup$ An example with $|P_i| = 3^5$ is given by Jack Schmidt here. $\endgroup$– Mikko KorhonenCommented Feb 11, 2019 at 13:06
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1 Answer
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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.
answered Feb 11, 2019 at 13:07