Finite Group DatabasebetaFinite Group DatabasebetaOrder 34688.
484 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 484 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. #31774551 | C2 | semidirect |
| 3. #31774550 | C2 | semidirect |
| 4. #31774276 | C2 | semidirect |
| 5. #31774137 | C2 | semidirect |
| 6. #31774103 | C2 | semidirect |
| 7. #31774062 | C2 | semidirect |
| 8. #31774056 | C2 | semidirect |
| 9. C4×#16864639 | C2 | semidirect |
| 10. #31773962 | C2 | semidirect |
| 11. #461×C271 | C2 | semidirect |
| 58. #16864639 | D4 | semidirect |
| 126. C4×C271 | #135 | semidirect |
| 138. C271 | #3283 | semidirect |
| 146. #461 | D271 | semidirect |
| 268. 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 |
| #31774551 | 2 |
| #31774550 | 2 |
| #31774276 | 2 |
| #31774137 | 2 |
| #31774103 | 2 |
| #31774062 | 2 |
| #31774056 | 2 |
| C4×#16864639 | 2 |
| #31773962 | 2 |
| #461×C271 | 2 |
| #3283 | 271 |