Finite Group DatabasebetaFinite Group DatabasebetaOrder 34688.
504 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 504 conjugacy classes of subgroups — too many to draw. Only its 141 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×#22576188 | C2 | semidirect |
| 2. C2×#22576168 | C2 | semidirect |
| 3. #31774478 | C2 | semidirect |
| 4. #31774466 | C2 | semidirect |
| 5. #31774151 | C2 | semidirect |
| 6. #31774144 | C2 | semidirect |
| 7. #31774134 | C2 | semidirect |
| 8. #31774127 | C2 | semidirect |
| 9. #31773891 | C2 | semidirect |
| 10. C2×#22576080 | C2 | semidirect |
| 11. #428×C271 | C2 | semidirect |
| 19. C2×#16864637 | C22 | semidirect |
| 21. C2×C8×D271 | C22 | semidirect |
| 25. #22576140 | C22 | semidirect |
| 29. #22576135 | C22 | semidirect |
| 32. #22576083 | C22 | semidirect |
| 33. #22576083 | C22 | semidirect |
| 36. #22576080 | C22 | semidirect |
| 37. #22576080 | C22 | semidirect |
| 41. #107×C271 | C22 | semidirect |
| 42. #106×C271 | C22 | semidirect |
| 77. M16×C271 | D4 | semidirect |
| 151. C271 | #3062 | semidirect |
| 161. #428 | D271 | semidirect |
| 187. #107 | C2×D271 | semidirect |
| 188. #106 | C2×D271 | semidirect |
| 220. M16 | D1084 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22576188 | 2 |
| C2×#22576168 | 2 |
| #31774478 | 2 |
| #31774466 | 2 |
| #31774151 | 2 |
| #31774144 | 2 |
| #31774134 | 2 |
| #31774127 | 2 |
| #31773891 | 2 |
| C2×#22576080 | 2 |
| #428×C271 | 2 |
| #3062 | 271 |