Finite Group DatabasebetaFinite Group Databasebeta| order | 3072 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C27 |
| direct product | C2×#72233208 |
| derived | C22⋊(C22⋊A4) ⋊ C22×C4 |
At least 6865 conjugacy classes of subgroups; only the 122 normal subgroups are shown.
This group has at least 6865 conjugacy classes of subgroups — too many to draw. Only its 122 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
120 conjugacy classes — view the full character table.
| maximal subgroup of | C2×C4×#87588⋊C2 |
| maximal normal subgroup of | C2×C4×#87588⋊C2 |
| maximal quotient of | C2×#72246416 |
Past the SmallGroups library coverage — no SmallGroups id.