Finite Group DatabasebetaFinite Group Databasebeta| order | 9216 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C32 · Schur multiplier (H2) = C25×C3 |
| direct product | C2×C3×#72209831 |
| Fitting | C2×C3×#6499874 ⋊ C3 |
| derived | #62817 ⋊ C22×C32 |
| Sylow | C2×#6499874 ⋊ C32 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C3 | #35346⋊C3 |
| commutator, cosocle, hypocenter | #62817 | C22×C32 |
| Frattini | C24 | C22×C3×C22⋊A4 |
| Fitting | C2×C3×#6499874 | C3 |
| hypercenter | C23×C3 | #85645 |
| LCS | G ▷ #62817 | |
| UCS | C1 ◁ C22×C3 ◁ C23×C3 | |
At least 10452 conjugacy classes of subgroups; only the 144 normal subgroups are shown.
This group has at least 10452 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.
216 conjugacy classes — view the full character table.
| maximal subgroup of | C2×C3×#72215845 |
Past the SmallGroups library coverage — no SmallGroups id.