Finite Group DatabasebetaFinite Group DatabasebetaOrder 31347.
926 conjugacy classes of subgroups; only the 454 normal subgroups are shown.
This group has 926 conjugacy classes of subgroups — too many to draw. Only its 454 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. #23782792 | C3 | semidirect |
| 3. C9×#11923956 | C3 | semidirect |
| 4. #11923957⋊C9 | C3 | semidirect |
| 6. #23782782 | C3 | semidirect |
| 7. #23782781 | C3 | semidirect |
| 8. C3×#16812500 | C3 | semidirect |
| 9. C9⋊C9×C43⋊C3 | C3 | semidirect |
| 10. C43×#6887 | C3 | semidirect |
| 11. #16812525 | C9 | semidirect |
| 37. #11923958 | C3×C9 | semidirect |
| 38. #11923957 | C3×C9 | semidirect |
| 39. #11923956 | C3×C9 | semidirect |
| 47. C9×C43⋊C3 | C3×C9 | semidirect |
| 49. C3×C9×C43 | C3×C9 | semidirect |
| 75. #6887 | C43⋊C3 | semidirect |
| 107. C43 | #10624864 | semidirect |
| 121. 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 |
|---|---|
| C3×#16812525 | 3 |
| #23782792 | 3 |
| C9×#11923956 | 3 |
| #11923957⋊C9 | 3 |
| #23782783 | 3 |
| #23782782 | 3 |
| #23782781 | 3 |
| C3×#16812500 | 3 |
| C9⋊C9×C43⋊C3 | 3 |
| C43×#6887 | 3 |
| #10624864 | 43 |