Finite Group DatabasebetaFinite Group DatabasebetaOrder 34688.
338 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 338 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. #31774627 | C2 | semidirect |
| 5. #31774180 | C2 | semidirect |
| 7. #31774104 | C2 | semidirect |
| 8. #31774027 | C2 | semidirect |
| 9. #31774001 | C2 | semidirect |
| 11. #487×C271 | C2 | semidirect |
| 116. C271 | #3369 | semidirect |
| 121. #487 | D271 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31774627 | 2 |
| #31774621 | 2 |
| #31774258 | 2 |
| #31774184 | 2 |
| #31774180 | 2 |
| #31774122 | 2 |
| #31774104 | 2 |
| #31774027 | 2 |
| #31774001 | 2 |
| C4×#16864643 | 2 |
| #487×C271 | 2 |
| #3369 | 271 |