Finite Group DatabasebetaFinite Group DatabasebetaOrder 31347.
318 conjugacy classes of subgroups; only the 58 normal subgroups are shown.
This group has 318 conjugacy classes of subgroups — too many to draw. Only its 58 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. #23782816 | C3 | semidirect |
| 2. #23782815 | C3 | semidirect |
| 3. C9×C32⋊(C43⋊C3) | C3 | semidirect |
| 4. #23782698 | C3 | semidirect |
| 5. #23782698 | C3 | semidirect |
| 6. #23782695 | C3 | semidirect |
| 7. #23782691 | C3 | semidirect |
| 8. #23782691 | C3 | semidirect |
| 9. #23782689 | C3 | semidirect |
| 10. #23782688 | C3 | semidirect |
| 11. #23782688 | C3 | semidirect |
| 13. C3×C43×#737 | C3 | semidirect |
| 94. C3×#737 | C43⋊C3 | semidirect |
| 140. C43 | #10624595 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23782816 | 3 |
| #23782815 | 3 |
| C9×C32⋊(C43⋊C3) | 3 |
| #23782698 | 3 |
| #23782695 | 3 |
| #23782691 | 3 |
| #23782689 | 3 |
| #23782688 | 3 |
| #23782686 | 3 |
| C3×C43×#737 | 3 |
| #10624595 | 43 |