Finite Group DatabasebetaFinite Group DatabasebetaOrder 1458.
503 conjugacy classes of subgroups; only the 68 normal subgroups are shown.
This group has 503 conjugacy classes of subgroups — too many to draw. Only its 68 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 | #92344 |
| commutator, cosocle, hypocenter | #6908 | C2×C3 |
| Frattini | C32 | C3×C3⋊(C3⋊D3) |
| Fitting | C3×#6908 | C2 |
| socle | C32 | C3⋊#272 |
| LCS | G ▷ #6908 | |
| UCS | C1 ◁ C3 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C3×#6908 | C2 | semidirect |
| 4. #92344 | C3 | direct (N × H) |
| 9. C3×#737 | D3 | semidirect |
| 10. C33×C9 | D3 | semidirect |
| 17. #6908 | C2×C3 | semidirect |
| 18. C3×#733 | D3 | semidirect |
| 19. C3×#732 | D3 | semidirect |
| 20. C3×#731 | D3 | semidirect |
| 21. C3×AΣL(1,𝔽27) | D3 | semidirect |
| 44. #737 | C3×D3 | semidirect |
| 57. C32×C9 | C3×D3 | semidirect |
| 63. #733 | C3×D3 | semidirect |
| 66. #732 | C3×D3 | semidirect |
| 70. #731 | C3×D3 | semidirect |
| 74. AΣL(1,𝔽27) | C3×D3 | semidirect |
| 198. C3 | #92344 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#6908 | 2 |
| C3×#4207 | 3 |
| C32×C3⋊D9 | 3 |
| #92344 | 3 |
| C3×#733⋊C2 | 3 |
| C3×#4185 | 3 |
| C3×#4184 | 3 |
| C3×#4183 | 3 |