Finite Group DatabasebetaFinite Group DatabasebetaOrder 31347.
836 conjugacy classes of subgroups; only the 316 normal subgroups are shown.
This group has 836 conjugacy classes of subgroups — too many to draw. Only its 316 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. #23782845 | C3 | semidirect |
| 3. #23782824 | C3 | semidirect |
| 4. #23782816 | C3 | semidirect |
| 5. #23782815 | C3 | semidirect |
| 6. #23782812 | C3 | semidirect |
| 8. 3−1+2×C43⋊C9 | C3 | semidirect |
| 9. C9×#11923958 | C3 | semidirect |
| 19. #16812500 | C32 | semidirect |
| 20. #16812499 | C32 | semidirect |
| 21. (C43⋊C9)⋊C9 | C32 | semidirect |
| 22. (C43⋊C9)⋊C9 | C32 | semidirect |
| 23. (C43⋊C9)⋊C9 | C32 | semidirect |
| 27. C9×C43⋊C9 | C32 | semidirect |
| 40. #11923958 | 3−1+2 | direct (N × H) |
| 56. 3−1+2×C43 | 3−1+2 | semidirect |
| 76. C9×C43 | C3×3−1+2 | semidirect |
| 80. C43⋊C9 | C3×3−1+2 | semidirect |
| 122. C43 | 3−1+22 | semidirect |
| 139. 3−1+2 | #11923958 | direct (N × H) |
| 167. C9 | C3×#11923958 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C32×#11923958 | 3 |
| #23782845 | 3 |
| #23782824 | 3 |
| #23782816 | 3 |
| #23782815 | 3 |
| #23782812 | 3 |
| #23782798 | 3 |
| 3−1+2×C43⋊C9 | 3 |
| C9×#11923958 | 3 |
| C32×3−1+2×C43 | 3 |
| 3−1+22 | 43 |