Finite Group DatabasebetaFinite Group DatabasebetaOrder 31347.
662 conjugacy classes of subgroups; only the 268 normal subgroups are shown.
This group has 662 conjugacy classes of subgroups — too many to draw. Only its 268 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. #23782837 | C3 | semidirect |
| 2. #23782834 | C3 | semidirect |
| 3. #23782829 | C3 | semidirect |
| 4. #23782823 | C3 | semidirect |
| 5. #23782820 | C3 | semidirect |
| 6. #23782819 | C3 | semidirect |
| 7. #23782818 | C3 | semidirect |
| 8. #23782817 | C3 | semidirect |
| 11. C9×#11923958 | C3 | semidirect |
| 12. C9×#11923958 | C3 | semidirect |
| 13. #23782782 | C3 | semidirect |
| 14. C3×C9×C43⋊C9 | C3 | semidirect |
| 151. C43 | #10624877 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23782837 | 3 |
| #23782834 | 3 |
| #23782829 | 3 |
| #23782823 | 3 |
| #23782820 | 3 |
| #23782819 | 3 |
| #23782818 | 3 |
| #23782817 | 3 |
| #23782806 | 3 |
| #23782800 | 3 |
| C9×#11923958 | 3 |
| #23782782 | 3 |
| C3×C9×C43⋊C9 | 3 |
| C9×H(3,𝔽3)×C43 | 3 |
| #10624877 | 43 |