Finite Group DatabasebetaFinite Group DatabasebetaOrder 31347.
824 conjugacy classes of subgroups; only the 310 normal subgroups are shown.
This group has 824 conjugacy classes of subgroups — too many to draw. Only its 310 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. #23782822 | C3 | semidirect |
| 2. #23782816 | C3 | semidirect |
| 3. #23782815 | C3 | semidirect |
| 5. C9×#11923958 | C3 | semidirect |
| 6. #23782782 | C3 | semidirect |
| 9. #16812500 | C32 | semidirect |
| 10. #16812499 | C32 | semidirect |
| 11. (C43⋊C9)⋊C9 | C32 | semidirect |
| 14. C9×C43⋊C9 | C32 | semidirect |
| 32. C3×C9×C43 | 3−1+2 | semidirect |
| 75. C43 | #10624872 | semidirect |
| 86. C3×C9 | #11923958 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23782822 | 3 |
| #23782816 | 3 |
| #23782815 | 3 |
| #23782798 | 3 |
| C9×#11923958 | 3 |
| #23782782 | 3 |
| C33×C9×C43 | 3 |
| #10624872 | 43 |