Finite Group DatabasebetaFinite Group DatabasebetaOrder 1944.
270 conjugacy classes of subgroups; only the 30 normal subgroups are shown.
This group has 270 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 | #10619756 |
| commutator, cosocle, hypocenter | #66361 | C2×C3 |
| Frattini | C32 | C3×C3⋊S4 |
| Fitting | C22×C3×H(3,𝔽3) | D3 |
| socle | C22×C32 | #272 |
| LCS | G ▷ #66361 | |
| UCS | C1 ◁ C3 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C3×#66361 | C2 | semidirect |
| 5. #10619756 | C3 | direct (N × H) |
| 9. C3×#1094 | D3 | semidirect |
| 10. C32×C22⋊C9 | D3 | semidirect |
| 15. #66361 | C2×C3 | semidirect |
| 45. #1094 | C3×D3 | semidirect |
| 50. C3×C22⋊C9 | C3×D3 | semidirect |
| 157. C22×C3 | #4184 | semidirect |
| 195. C22 | C3×#4184 | semidirect |
| 202. C3 | #10619756 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#66361 | 2 |
| C32×(C22⋊C9)⋊C2 | 3 |
| C3×((C22⋊C9)⋊C2)⋊C3 | 3 |
| C3×#638⋊C3 | 3 |
| #10619756 | 3 |
| C3×#4184 | 4 |