Finite Group DatabasebetaFinite Group DatabasebetaOrder 31347.
1052 conjugacy classes of subgroups; only the 472 normal subgroups are shown.
This group has 1052 conjugacy classes of subgroups — too many to draw. Only its 472 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. #23782782 | C3 | semidirect |
| 3. #23782781 | C3 | semidirect |
| 4. #23782780 | C3 | semidirect |
| 5. #23782779 | C3 | semidirect |
| 6. C9⋊C9×C43⋊C3 | C3 | semidirect |
| 8. C92×C43⋊C3 | C3 | semidirect |
| 9. C43×#6887 | C3 | semidirect |
| 12. C3×C9×C43⋊C3 | C9 | semidirect |
| 18. #16812500 | C32 | semidirect |
| 19. #16812499 | C32 | semidirect |
| 20. (C43⋊C9)⋊C9 | C32 | semidirect |
| 23. C9×C43⋊C9 | C32 | semidirect |
| 24. C9×C43⋊C9 | C32 | semidirect |
| 26. C43×C9⋊C9 | C32 | semidirect |
| 28. C92×C43 | C32 | semidirect |
| 33. C3×C43⋊C9 | C3×C9 | semidirect |
| 40. C9×C43⋊C3 | C3×C9 | semidirect |
| 41. C9×C43⋊C3 | C3×C9 | semidirect |
| 43. C3×C9×C43 | C3×C9 | semidirect |
| 67. #6887 | C43⋊C3 | direct (N × H) |
| 75. C43⋊C3 | #6887 | direct (N × H) |
| 88. C9⋊C9 | C3×C43⋊C3 | semidirect |
| 94. C92 | C3×C43⋊C3 | semidirect |
| 95. C43 | C3×#6887 | semidirect |
| 110. C3×C9 | C9×C43⋊C3 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C32×C9×C43⋊C3 | 3 |
| #23782782 | 3 |
| #23782781 | 3 |
| #23782780 | 3 |
| #23782779 | 3 |
| C9⋊C9×C43⋊C3 | 3 |
| C32⋊C9×C43⋊C3 | 3 |
| C92×C43⋊C3 | 3 |
| C43×#6887 | 3 |
| C3×#6887 | 43 |