Finite Group DatabasebetaFinite Group DatabasebetaOrder 2916.
574 conjugacy classes of subgroups; only the 62 normal subgroups are shown.
This group has 574 conjugacy classes of subgroups — too many to draw. Only its 62 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 | #13091158 |
| commutator, cosocle, hypocenter | C34 | C22×C32 |
| Frattini | C33 | C2×C32×D3 |
| Fitting | C2×#10624761 | C2 |
| socle | C2×C3 | #92258 |
| LCS | G ▷ C34 | |
| UCS | C1 ◁ C2 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #13091158 | C2 | direct (N × H) |
| 2. C2×#10624761 | C2 | semidirect |
| 4. C2×C3⋊#4175 | C3 | semidirect |
| 5. C2×C3⋊#4175 | C3 | semidirect |
| 6. C2×C3⋊#4175 | C3 | semidirect |
| 7. C2×C3⋊#4175 | C3 | semidirect |
| 8. #10624761 | C22 | semidirect |
| 9. C2×H(5,𝔽3) | D3 | semidirect |
| 15. C2×C3×AΣL(1,𝔽27) | C2×C3 | semidirect |
| 16. C2×C3×AΣL(1,𝔽27) | C2×C3 | semidirect |
| 17. C2×C3×AΣL(1,𝔽27) | C2×C3 | semidirect |
| 18. C2×C3×AΣL(1,𝔽27) | C2×C3 | semidirect |
| 19. C3⋊#4175 | C2×C3 | semidirect |
| 20. C3⋊#4175 | C2×C3 | semidirect |
| 21. C3⋊#4175 | C2×C3 | semidirect |
| 22. C3⋊#4175 | C2×C3 | semidirect |
| 23. C2×C3⋊(C3⋊(C3⋊D3)) | C32 | semidirect |
| 36. H(5,𝔽3) | C2×D3 | semidirect |
| 41. C3×AΣL(1,𝔽27) | C22×C3 | semidirect |
| 42. C3×AΣL(1,𝔽27) | C22×C3 | semidirect |
| 43. C3×AΣL(1,𝔽27) | C22×C3 | semidirect |
| 44. C3×AΣL(1,𝔽27) | C22×C3 | semidirect |
| 45. C2×C34 | C2×C32 | semidirect |
| 46. C3⋊(C3⋊(C3⋊D3)) | C2×C32 | semidirect |
| 114. C34 | C22×C32 | semidirect |
| 428. C2 | #13091158 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #13091158 | 2 |
| C2×#10624761 | 2 |
| C2×#92391 | 3 |
| C2×C3⋊#4175 | 3 |