Finite Group DatabasebetaFinite Group DatabasebetaOrder 34688.
360 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 360 conjugacy classes of subgroups — too many to draw. Only its 113 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. #31774600 | C2 | semidirect |
| 2. #31774224 | C2 | semidirect |
| 3. #31774212 | C2 | semidirect |
| 4. #31774194 | C2 | semidirect |
| 5. #31774151 | C2 | semidirect |
| 6. C4×D2168 | C2 | semidirect |
| 7. #31773976 | C2 | semidirect |
| 8. #31773936 | C2 | semidirect |
| 9. #499×C271 | C2 | semidirect |
| 102. C271 | #3355 | semidirect |
| 105. #499 | D271 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31774600 | 2 |
| #31774224 | 2 |
| #31774212 | 2 |
| #31774194 | 2 |
| #31774151 | 2 |
| C4×D2168 | 2 |
| #31773976 | 2 |
| #31773936 | 2 |
| #499×C271 | 2 |
| #3355 | 271 |