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

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