Finite Group DatabasebetaFinite Group DatabasebetaOrder 34688.
482 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 482 conjugacy classes of subgroups — too many to draw. Only its 123 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. C2×#22576179 | C2 | semidirect |
| 2. C2×Q16×D271 | C2 | semidirect |
| 3. #31774555 | C2 | semidirect |
| 4. #31774135 | C2 | semidirect |
| 5. #31774130 | C2 | semidirect |
| 6. #31774116 | C2 | semidirect |
| 7. #31774056 | C2 | semidirect |
| 8. #31774034 | C2 | semidirect |
| 9. C4×Dic1084 | C2 | semidirect |
| 10. C8×D1084 | C2 | semidirect |
| 11. #495×C271 | C2 | semidirect |
| 54. Dic1084 | D4 | semidirect |
| 120. C2×D271 | #135 | semidirect |
| 136. C271 | #3285 | semidirect |
| 141. #495 | D271 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22576179 | 2 |
| C2×Q16×D271 | 2 |
| #31774555 | 2 |
| #31774135 | 2 |
| #31774130 | 2 |
| #31774116 | 2 |
| #31774056 | 2 |
| #31774034 | 2 |
| C4×Dic1084 | 2 |
| C8×D1084 | 2 |
| #495×C271 | 2 |
| #3285 | 271 |