Finite Group DatabasebetaFinite Group DatabasebetaOrder 31347.
5804 conjugacy classes of subgroups; only the 2920 normal subgroups are shown.
This group has 5804 conjugacy classes of subgroups — too many to draw. Only its 2920 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×#16812525 | C3 | direct (N × H) |
| 2. C32×#11923958 | C3 | semidirect |
| 3. C32×#11923957 | C3 | semidirect |
| 4. C32×#11923956 | C3 | semidirect |
| 6. C32×C9×C43⋊C3 | C3 | semidirect |
| 7. C33×C9×C43 | C3 | semidirect |
| 9. #16812525 | C32 | direct (N × H) |
| 10. C3×#11923958 | C32 | semidirect |
| 11. C3×#11923957 | C32 | semidirect |
| 12. C3×#11923956 | C32 | semidirect |
| 15. C3×C9×C43⋊C3 | C32 | semidirect |
| 20. C32×C9×C43 | C32 | semidirect |
| 23. #11923958 | C33 | semidirect |
| 24. #11923957 | C33 | semidirect |
| 25. #11923956 | C33 | semidirect |
| 28. C9×C43⋊C3 | C33 | semidirect |
| 35. C3×C9×C43 | C33 | semidirect |
| 38. C32×C43 | #737 | semidirect |
| 53. C33×C9 | C43⋊C3 | semidirect |
| 55. C3×C43 | C3×#737 | semidirect |
| 70. C32×C9 | C3×C43⋊C3 | semidirect |
| 71. C43 | C32×#737 | semidirect |
| 86. C3×C9 | C32×C43⋊C3 | semidirect |
| 90. C32 | #16812525 | direct (N × H) |
| 99. C3 | C3×#16812525 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#16812525 | 3 |
| C32×#11923958 | 3 |
| C32×#11923957 | 3 |
| C32×#11923956 | 3 |
| C32×C32⋊(C43⋊C3) | 3 |
| C32×C9×C43⋊C3 | 3 |
| C33×C9×C43 | 3 |
| C32×#737 | 43 |