Finite Group DatabasebetaFinite Group DatabasebetaOrder 31347.
1064 conjugacy classes of subgroups; only the 274 normal subgroups are shown.
This group has 1064 conjugacy classes of subgroups — too many to draw. Only its 274 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C3×#16812526 | C3 | semidirect |
| 2. C3×#16812524 | C3 | semidirect |
| 3. C33×C43⋊C9 | C3 | semidirect |
| 4. #23782873 | C3 | direct (N × H) |
| 5. C3×#16812514 | C3 | semidirect |
| 6. C3×#16812512 | C3 | semidirect |
| 7. C3×#16812511 | C3 | semidirect |
| 8. C3×#16812509 | C3 | semidirect |
| 9. C3×#16812507 | C3 | semidirect |
| 10. C3×C43×AΣL(1,𝔽27) | C3 | semidirect |
| 12. #16812526 | C32 | semidirect |
| 14. #16812524 | C32 | semidirect |
| 28. C32×C43⋊C9 | C32 | semidirect |
| 30. #16812514 | C32 | semidirect |
| 31. #16812512 | C32 | semidirect |
| 32. #16812511 | C32 | semidirect |
| 33. #16812509 | C32 | semidirect |
| 34. #16812507 | C32 | semidirect |
| 38. C43×AΣL(1,𝔽27) | C32 | semidirect |
| 105. C3×AΣL(1,𝔽27) | C43⋊C3 | semidirect |
| 110. C3×C43 | #6908 | semidirect |
| 140. AΣL(1,𝔽27) | C3×C43⋊C3 | semidirect |
| 141. C43 | C3×#6908 | semidirect |
| 203. C3 | #23782873 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#16812526 | 3 |
| C3×#16812524 | 3 |
| C33×C43⋊C9 | 3 |
| #23782873 | 3 |
| C3×#16812514 | 3 |
| C3×#16812512 | 3 |
| C3×#16812511 | 3 |
| C3×#16812509 | 3 |
| C3×#16812507 | 3 |
| C3×C43×AΣL(1,𝔽27) | 3 |
| C3×#6908 | 43 |