Finite Group DatabasebetaFinite Group DatabasebetaOrder 34688.
494 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 494 conjugacy classes of subgroups — too many to draw. Only its 125 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×#22576181 | C2 | semidirect |
| 2. #31774567 | C2 | semidirect |
| 3. #31774550 | C2 | semidirect |
| 4. #31774123 | C2 | semidirect |
| 5. #31774104 | C2 | semidirect |
| 6. #31774089 | C2 | semidirect |
| 7. #31774056 | C2 | semidirect |
| 8. #31774041 | C2 | semidirect |
| 9. C4×#16864643 | C2 | semidirect |
| 10. C8×D1084 | C2 | semidirect |
| 11. #492×C271 | C2 | semidirect |
| 57. #16864643 | D4 | semidirect |
| 127. C4×C271 | #135 | semidirect |
| 140. C271 | #3284 | semidirect |
| 145. #492 | D271 | semidirect |
| 272. C4 | #22576181 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22576181 | 2 |
| #31774567 | 2 |
| #31774550 | 2 |
| #31774123 | 2 |
| #31774104 | 2 |
| #31774089 | 2 |
| #31774056 | 2 |
| #31774041 | 2 |
| C4×#16864643 | 2 |
| C8×D1084 | 2 |
| #492×C271 | 2 |
| #3284 | 271 |