Finite Group DatabasebetaFinite Group DatabasebetaOrder 31347.
202 conjugacy classes of subgroups; only the 46 normal subgroups are shown.
This group has 202 conjugacy classes of subgroups — too many to draw. Only its 46 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. #23782878 | C3 | semidirect |
| 2. #23782878 | C3 | semidirect |
| 3. #23782875 | C3 | semidirect |
| 4. C9⋊C9×C43⋊C3 | C3 | semidirect |
| 5. #23782766 | C3 | semidirect |
| 6. #23782765 | C3 | semidirect |
| 7. #23782764 | C3 | semidirect |
| 8. #23782763 | C3 | semidirect |
| 9. #23782762 | C3 | semidirect |
| 10. #23782757 | C3 | semidirect |
| 11. #23782756 | C3 | semidirect |
| 12. #23782755 | C3 | semidirect |
| 13. C43×#6883 | C3 | semidirect |
| 95. #6883 | C43⋊C3 | semidirect |
| 133. C43 | #10624850 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23782878 | 3 |
| #23782875 | 3 |
| C9⋊C9×C43⋊C3 | 3 |
| #23782766 | 3 |
| #23782765 | 3 |
| #23782764 | 3 |
| #23782763 | 3 |
| #23782762 | 3 |
| #23782757 | 3 |
| #23782756 | 3 |
| #23782755 | 3 |
| C43×#6883 | 3 |
| #10624850 | 43 |