Finite Group DatabasebetaFinite Group Databasebeta| order | 7056 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C32 · Schur multiplier (H2) = C23×C3 |
| direct product | C3×#72210376 |
| Fitting | C22×C3×C72 ⋊ C22×C3 |
| Hall | #11716115 ⋊ C32 |
| Hall | C3×#3861 ⋊ C2×D4 |
| Sylow | C72 ⋊ C2×C32×D4 |
936 conjugacy classes of subgroups; only the 144 normal subgroups are shown.
This group has 936 conjugacy classes of subgroups — too many to draw. Only its 144 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
156 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#72210376, C3×#72222121, C2×C3×#72210376, … |
| maximal normal subgroup of | D3×#72210376, C2×C3×#72210376, C32×#72210376 |
| maximal quotient of | C3×#72222121, C2×C3×#72210376, C32×#72210376 |
Past the SmallGroups library coverage — no SmallGroups id.