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We investigate the symmetric spaces associated to the family of semidihedral groups of order 2 n . We begin this study by analyzing the structure of the automorphism group and by determining which automorphims are involutions. We then determine the symmetric spaces corresponding to each involution and the orbits of the fixed-point groups on these spaces. MSC2010: 20D15, 53C35.doi:10.2140/involve.2017.10.665 fatcat:qhc4jcqkunf6vienv5jhjkyjiy