Finite Group DatabasebetaFinite Group Databasebeta| order | 2016 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C3 · Schur multiplier (H2) = C23 |
| direct product | D3×#1141⋊C3 |
| Fitting | C3×C7×D4 ⋊ C22×C3 |
| Hall | C3×ΓL(1,𝔽8) ⋊ C2×D8 |
| Sylow | C7 ⋊ C3×D3×D8 |
326 conjugacy classes of subgroups; only the 73 normal subgroups are shown.
This group has 326 conjugacy classes of subgroups — too many to draw. Only its 73 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 168 |
78 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#6495⋊C3, D3×#6512⋊C3, D3×#6477⋊C3, … |
| maximal normal subgroup of | D3×#6495⋊C3, D3×#6512⋊C3, D3×#6477⋊C3, … |
| maximal quotient of | #72254228, #72254233 |
Past the SmallGroups library coverage — no SmallGroups id.