Finite Group DatabasebetaFinite Group DatabasebetaOrder 31347.
472 conjugacy classes of subgroups; only the 88 normal subgroups are shown.
This group has 472 conjugacy classes of subgroups — too many to draw. Only its 88 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. C32×C9×C43⋊C3 | C3 | semidirect |
| 3. C9×#11923958 | C3 | semidirect |
| 4. C9×C32⋊(C43⋊C3) | C3 | semidirect |
| 5. #23782725 | C3 | semidirect |
| 6. 3−1+2⋊(C43⋊C9) | C3 | semidirect |
| 7. #23782719 | C3 | semidirect |
| 8. #23782711 | C3 | semidirect |
| 9. C9×3−1+2×C43 | C3 | semidirect |
| 18. #16812508 | C9 | direct (N × H) |
| 34. C32×C43⋊C3 | C3×C9 | semidirect |
| 36. #11923958 | C3×C9 | semidirect |
| 38. C32⋊(C43⋊C3) | C3×C9 | semidirect |
| 49. 3−1+2×C43 | C3×C9 | semidirect |
| 72. C9×C43 | AΣL(1,𝔽27) | semidirect |
| 80. C9×3−1+2 | C43⋊C3 | semidirect |
| 112. C43 | C9×AΣL(1,𝔽27) | semidirect |
| 123. 3−1+2 | C9×C43⋊C3 | semidirect |
| 159. C9 | #16812508 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C32×C9×C43⋊C3 | 3 |
| C3×#16812508 | 3 |
| C9×#11923958 | 3 |
| C9×C32⋊(C43⋊C3) | 3 |
| #23782725 | 3 |
| 3−1+2⋊(C43⋊C9) | 3 |
| #23782719 | 3 |
| #23782711 | 3 |
| C9×3−1+2×C43 | 3 |
| C9×AΣL(1,𝔽27) | 43 |