Finite Group DatabasebetaFinite Group DatabasebetaOrder 34432.
386 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 386 conjugacy classes of subgroups — too many to draw. Only its 115 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. #31771160 | C2 | semidirect |
| 3. #31770898 | C2 | semidirect |
| 4. #31770886 | C2 | semidirect |
| 5. #31770885 | C2 | semidirect |
| 6. #31770854 | C2 | semidirect |
| 7. #31770848 | C2 | semidirect |
| 8. #31770807 | C2 | semidirect |
| 9. #31770803 | C2 | semidirect |
| 10. #31770627 | C2 | semidirect |
| 11. #461×C269 | C2 | semidirect |
| 142. C269 | #3254 | semidirect |
| 152. #461 | D269 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31771160 | 2 |
| #31771152 | 2 |
| #31770898 | 2 |
| #31770886 | 2 |
| #31770885 | 2 |
| #31770854 | 2 |
| #31770848 | 2 |
| #31770807 | 2 |
| #31770803 | 2 |
| #31770627 | 2 |
| #461×C269 | 2 |
| #3254 | 269 |