Finite Group DatabasebetaFinite Group Databasebeta| order | 5184 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C8 · Schur multiplier (H2) = C22×C4 |
| direct product | C2×#72213723 |
| derived, Sylow | C34 ⋊ C2×C4×C8 |
1066 conjugacy classes of subgroups; only the 102 normal subgroups are shown.
This group has 1066 conjugacy classes of subgroups — too many to draw. Only its 102 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
96 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#72219722, #72220269, #72220308, … |
| maximal normal subgroup of | C2×#72219722, #72220269, #72220308, … |
Past the SmallGroups library coverage — no SmallGroups id.