Finite Group DatabasebetaFinite Group DatabasebetaOrder 1944.
650 conjugacy classes of subgroups; only the 64 normal subgroups are shown.
This group has 650 conjugacy classes of subgroups — too many to draw. Only its 64 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | #11757748 |
| commutator, cosocle, hypocenter | C9×H(3,𝔽3) | C23 |
| Frattini | C32 | C2×#1113 |
| Fitting | C2×C9×H(3,𝔽3) | C22 |
| socle | C2×C32 | #1113 |
| LCS | G ▷ C9×H(3,𝔽3) | |
| UCS | C1 ◁ C2 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×C9×#272 | C2 | semidirect |
| 2. C2×#92297 | C2 | semidirect |
| 3. #11757748 | C2 | direct (N × H) |
| 6. C2×C9×H(3,𝔽3) | C22 | semidirect |
| 7. C9×#272 | C22 | semidirect |
| 8. #92297 | C22 | semidirect |
| 9. C2×C3⋊(C3⋊D9) | D3 | semidirect |
| 18. C9×H(3,𝔽3) | C23 | semidirect |
| 25. C2×C32×C9 | C2×D3 | semidirect |
| 26. C3⋊(C3⋊D9) | C2×D3 | semidirect |
| 41. C2×#272 | D9 | semidirect |
| 55. C32×C9 | C22×D3 | semidirect |
| 71. C2×H(3,𝔽3) | C2×D9 | semidirect |
| 78. #272 | C2×D9 | semidirect |
| 114. H(3,𝔽3) | C22×D9 | semidirect |
| 132. C2×C32 | D3×D9 | semidirect |
| 151. C2×C9 | ((C3⋊D3)⋊C3)⋊C2 | semidirect |
| 176. C32 | C2×D3×D9 | semidirect |
| 180. C9 | C2×((C3⋊D3)⋊C3)⋊C2 | semidirect |
| 212. C2 | #11757748 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C9×#272 | 2 |
| C2×#92297 | 2 |
| #11757748 | 2 |
| C2×#66432 | 3 |
| C2×D3×C3⋊D9 | 3 |