Finite Group DatabasebetaFinite Group Databasebeta| order | 12288 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C27 |
| direct product | C4×#72209832 |
| Fitting | C4×#6499874 ⋊ D3 |
| derived | #11710730 ⋊ C22×C4 |
At least 31976 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has at least 31976 conjugacy classes of subgroups — too many to draw. Only its 105 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
180 conjugacy classes — view the full character table.
| maximal subgroup of | C4×#72215896 |
| automorphism group of | C22×C5×D4 |
Past the SmallGroups library coverage — no SmallGroups id.