Finite Group DatabasebetaFinite Group DatabasebetaOrder 31347.
236 conjugacy classes of subgroups; only the 49 normal subgroups are shown.
This group has 236 conjugacy classes of subgroups — too many to draw. Only its 49 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. #23782819 | C3 | semidirect |
| 2. #23782800 | C3 | semidirect |
| 3. H(3,𝔽3)×C43⋊C9 | C3 | semidirect |
| 4. #23782783 | C3 | semidirect |
| 5. #23782702 | C3 | semidirect |
| 6. #23782702 | C3 | semidirect |
| 7. #23782700 | C3 | semidirect |
| 8. #23782696 | C3 | semidirect |
| 9. #23782695 | C3 | semidirect |
| 10. #23782695 | C3 | semidirect |
| 11. #23782686 | C3 | semidirect |
| 12. #23782686 | C3 | semidirect |
| 13. C43×#6856 | C3 | semidirect |
| 104. #6856 | C43⋊C3 | semidirect |
| 138. C43 | #10624622 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23782819 | 3 |
| #23782800 | 3 |
| H(3,𝔽3)×C43⋊C9 | 3 |
| #23782783 | 3 |
| #23782702 | 3 |
| #23782700 | 3 |
| #23782696 | 3 |
| #23782695 | 3 |
| #23782686 | 3 |
| C43×#6856 | 3 |
| #10624622 | 43 |