Finite Group DatabasebetaFinite Group DatabasebetaOrder 31347.
200 conjugacy classes of subgroups; only the 58 normal subgroups are shown.
This group has 200 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. #23782815 | C3 | semidirect |
| 2. C9×#11923958 | C3 | semidirect |
| 3. #23782782 | C3 | semidirect |
| 4. C43⋊#6862 | C3 | semidirect |
| 5. #23782700 | C3 | semidirect |
| 8. #23782694 | C3 | semidirect |
| 9. #23782694 | C3 | semidirect |
| 10. #23782693 | C3 | semidirect |
| 11. #23782693 | C3 | semidirect |
| 128. C43 | #10624621 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23782815 | 3 |
| C9×#11923958 | 3 |
| #23782782 | 3 |
| C43⋊#6862 | 3 |
| #23782700 | 3 |
| #23782695 | 3 |
| #23782694 | 3 |
| #23782693 | 3 |
| #23782689 | 3 |
| C43×C9⋊H(3,𝔽3) | 3 |
| #10624621 | 43 |