Abstract
For a finite group G, let ν(G) denote the number of conjugacy classes of non-normal subgroups of G. We determine all finite non-soluble groups G with ν(G) < 14. As a consequence, all finite groups G with ν(G) ≤ 6 or \({\nu(G)\in \{ 8,11,12\}}\) are soluble.
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Brandl, R. Non-soluble groups with few conjugacy classes of non-normal subgroups. Beitr Algebra Geom 54, 493–501 (2013). https://doi.org/10.1007/s13366-012-0087-5
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DOI: https://doi.org/10.1007/s13366-012-0087-5