Finite Group DatabasebetaFinite Group DatabasebetaOrder 34688.
504 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 504 conjugacy classes of subgroups — too many to draw. Only its 133 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×#22576185 | C2 | semidirect |
| 2. C2×#22576166 | C2 | semidirect |
| 3. #31774475 | C2 | semidirect |
| 4. #31774466 | C2 | semidirect |
| 5. #31774149 | C2 | semidirect |
| 6. #31774146 | C2 | semidirect |
| 7. #31774132 | C2 | semidirect |
| 8. #31774129 | C2 | semidirect |
| 9. #31773940 | C2 | semidirect |
| 10. C2×#22576082 | C2 | semidirect |
| 11. #416×C271 | C2 | semidirect |
| 19. C2×#16864637 | C22 | semidirect |
| 20. C2×C8×D271 | C22 | semidirect |
| 24. #22576136 | C22 | semidirect |
| 29. #22576131 | C22 | semidirect |
| 32. #22576093 | C22 | semidirect |
| 33. #22576091 | C22 | semidirect |
| 39. #103×C271 | C22 | semidirect |
| 40. #103×C271 | C22 | semidirect |
| 41. #102×C271 | C22 | semidirect |
| 42. #102×C271 | C22 | semidirect |
| 60. #16864638 | D4 | semidirect |
| 151. C271 | #3062 | semidirect |
| 162. #416 | D271 | semidirect |
| 189. #103 | C2×D271 | semidirect |
| 190. #103 | C2×D271 | semidirect |
| 193. #102 | C2×D271 | semidirect |
| 194. #102 | C2×D271 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22576185 | 2 |
| C2×#22576166 | 2 |
| #31774475 | 2 |
| #31774466 | 2 |
| #31774149 | 2 |
| #31774146 | 2 |
| #31774132 | 2 |
| #31774129 | 2 |
| #31773940 | 2 |
| C2×#22576082 | 2 |
| #416×C271 | 2 |
| #3062 | 271 |