Finite Group DatabasebetaFinite Group DatabasebetaOrder 31347.
2996 conjugacy classes of subgroups; only the 652 normal subgroups are shown.
This group has 2996 conjugacy classes of subgroups — too many to draw. Only its 652 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×C9×C43⋊C3 | C3 | semidirect |
| 3. C3×C32⋊(C43⋊C9) | C3 | semidirect |
| 4. C3×(C3×C43⋊C3)⋊C9 | C3 | semidirect |
| 5. C32⋊C9×C43⋊C3 | C3 | direct (N × H) |
| 6. C3×C43×C32⋊C9 | C3 | semidirect |
| 9. C33×C43⋊C3 | C9 | semidirect |
| 13. C32×C43⋊C9 | C32 | semidirect |
| 15. C3×C9×C43⋊C3 | 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 |
| 27. C32×C43⋊C3 | C3×C9 | semidirect |
| 28. C32×C43⋊C3 | C3×C9 | semidirect |
| 34. C3×C43⋊C9 | C33 | semidirect |
| 38. C33×C43 | C3×C9 | semidirect |
| 42. C3×C9×C43 | C33 | semidirect |
| 48. C32×C43 | C32×C9 | semidirect |
| 56. C3×C43⋊C3 | C32⋊C9 | direct (N × H) |
| 58. C3×C43⋊C3 | C32×C9 | semidirect |
| 68. C3×C32⋊C9 | C43⋊C3 | direct (N × H) |
| 70. C3×C43 | C3×C32⋊C9 | semidirect |
| 75. C43⋊C3 | C3×C32⋊C9 | direct (N × H) |
| 86. C32×C9 | C3×C43⋊C3 | semidirect |
| 89. C32⋊C9 | C3×C43⋊C3 | direct (N × H) |
| 90. C43 | C32×C32⋊C9 | semidirect |
| 105. C33 | C9×C43⋊C3 | semidirect |
| 112. C3×C9 | C32×C43⋊C3 | semidirect |
| 126. C32 | C3×C9×C43⋊C3 | semidirect |
| 135. C3 | C32⋊C9×C43⋊C3 | 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×C9×C43⋊C3 | 3 |
| C3×C32⋊(C43⋊C9) | 3 |
| C3×(C3×C43⋊C3)⋊C9 | 3 |
| C32⋊C9×C43⋊C3 | 3 |
| C3×C43×C32⋊C9 | 3 |
| C32×C32⋊C9 | 43 |