Finite Group DatabasebetaFinite Group DatabasebetaOrder 31347.
2636 conjugacy classes of subgroups; only the 382 normal subgroups are shown.
This group has 2636 conjugacy classes of subgroups — too many to draw. Only its 382 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 |
|---|---|---|
| 2. C32×#11923957 | C3 | semidirect |
| 3. #23782797 | C3 | direct (N × H) |
| 4. C3×C32⋊(C43⋊C9) | C3 | semidirect |
| 5. C3×(C3×C43⋊C3)⋊C9 | C3 | semidirect |
| 6. C3×C43×C32⋊C9 | C3 | semidirect |
| 14. C3×#11923957 | C32 | semidirect |
| 15. C32×C43⋊C9 | C32 | semidirect |
| 16. C32⋊(C43⋊C9) | C32 | semidirect |
| 17. (C3×C43⋊C3)⋊C9 | C32 | semidirect |
| 19. C32×C9×C43 | C32 | semidirect |
| 20. C43×C32⋊C9 | C32 | semidirect |
| 31. C32×C43⋊C3 | 3−1+2 | semidirect |
| 36. C3×C43⋊C9 | C33 | semidirect |
| 39. C33×C43 | 3−1+2 | semidirect |
| 43. C3×C9×C43 | C33 | semidirect |
| 51. C32×C43 | C3×3−1+2 | semidirect |
| 62. C3×C43⋊C3 | C3×3−1+2 | semidirect |
| 70. C3×C32⋊C9 | C43⋊C3 | semidirect |
| 72. C3×C43 | #6891 | semidirect |
| 88. C32×C9 | C3×C43⋊C3 | semidirect |
| 91. C32⋊C9 | C3×C43⋊C3 | semidirect |
| 92. C43 | C3×#6891 | semidirect |
| 108. C33 | #11923957 | semidirect |
| 115. C3×C9 | C32×C43⋊C3 | semidirect |
| 132. C32 | C3×#11923957 | semidirect |
| 139. C3 | #23782797 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C34×C43⋊C3 | 3 |
| C32×#11923957 | 3 |
| #23782797 | 3 |
| C3×C32⋊(C43⋊C9) | 3 |
| C3×(C3×C43⋊C3)⋊C9 | 3 |
| C3×C43×C32⋊C9 | 3 |
| C3×#6891 | 43 |