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Second-metacyclic finite 2-groups

Croatian Mathematical Society and Department of Mathematics, University of Zagreb
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  • Finite Group
  • P-Group
  • Metacyclic
  • Second-Maximal Subgroup
  • Second-Metacyclic Group.


Second-metacyclic finite 2-groups are finite 2-groups with some non-metacyclic maximal subgroup and with all second-maximal subgroups being metacyclic. According to a known result there are only four non-metacyclic finite 2-groups with all maximal subgroups being metacyclic. The groups pointed in the title should contain some of these groups as a subgroup of index 2. There are seventeen second-maximal finite 2-groups, four among them being of order 16, ten of order 32 and three of order 64.

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