Finite Group DatabasebetaFinite Group DatabasebetaOrder 1944.
276 conjugacy classes of subgroups; only the 30 normal subgroups are shown.
This group has 276 conjugacy classes of subgroups — too many to draw. Only its 30 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | #10620047 |
| commutator, cosocle, hypocenter | C32⋊(C22⋊C9) | C2×C3 |
| Frattini | C32 | C3×C3⋊S4 |
| Fitting | C22×C3×H(3,𝔽3) | D3 |
| socle | C22×C32 | C3×C3⋊D3 |
| LCS | G ▷ C32⋊(C22⋊C9) | |
| UCS | C1 ◁ C3 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #11757833 | C2 | semidirect |
| 5. #10619761 | C3 | semidirect |
| 9. C3×#1094 | D3 | semidirect |
| 10. C32×C22⋊C9 | D3 | semidirect |
| 15. C32⋊(C22⋊C9) | C2×C3 | semidirect |
| 168. C22 | #92304 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11757833 | 2 |
| C32×(C22⋊C9)⋊C2 | 3 |
| C3×((C22⋊C9)⋊C2)⋊C3 | 3 |
| C3×#638⋊C3 | 3 |
| #10619761 | 3 |
| #92304 | 4 |