Geodesic
Two Nonconjugate Embeddings of the Group $S_3\times\mathbb Z_2$ into the Cremona Group
Trudy Matematicheskogo Instituta imeni V.A. Steklova, Number theory, algebra, and algebraic geometry, Tome 241 (2003), pp. 105-109 
V. A. Iskovskikh. Two Nonconjugate Embeddings of the Group $S_3\times\mathbb Z_2$ into the Cremona Group. Trudy Matematicheskogo Instituta imeni V.A. Steklova, Number theory, algebra, and algebraic geometry, Tome 241 (2003), pp. 105-109. http://geodesic.mathdoc.fr/item/TM_2003_241_a4/
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     title = {Two {Nonconjugate} {Embeddings} of the {Group} $S_3\times\mathbb Z_2$ into the {Cremona} {Group}},
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Voir la notice du chapitre de livre provenant de la source Math-Net.Ru

A concrete example of two isomorphic nonconjugate subgroups in the two-dimensional Cremona group is presented.

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[2] Iskovskikh V. A., “Faktorizatsiya biratsionalnykh otobrazhenii ratsionalnykh poverkhnostei s tochki zreniya teorii Mori”, UMN, 51:4 (1996), 3–72 | MR | Zbl

[3] Manin Yu. I., “Ratsionalnye poverkhnosti nad sovershennymi polyami, II”, Mat. sb., 72:2 (1967), 161–192 | MR | Zbl