Finite Group DatabasebetaFinite Group DatabasebetaOrder 31347.
204 conjugacy classes of subgroups; only the 52 normal subgroups are shown.
This group has 204 conjugacy classes of subgroups — too many to draw. Only its 52 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. #23782817 | C3 | semidirect |
| 2. #23782817 | C3 | semidirect |
| 4. #23782779 | C3 | semidirect |
| 5. C43⋊#6862 | C3 | semidirect |
| 6. #23782702 | C3 | semidirect |
| 8. #23782694 | C3 | semidirect |
| 9. #23782693 | C3 | semidirect |
| 10. #23782692 | C3 | semidirect |
| 11. #23782692 | C3 | semidirect |
| 128. C43 | #10624606 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23782817 | 3 |
| H(3,𝔽3)×C43⋊C9 | 3 |
| #23782779 | 3 |
| C43⋊#6862 | 3 |
| #23782702 | 3 |
| #23782695 | 3 |
| #23782694 | 3 |
| #23782693 | 3 |
| #23782692 | 3 |
| #23782689 | 3 |
| C43×#6859 | 3 |
| #10624606 | 43 |