Finite Group DatabasebetaFinite Group DatabasebetaOrder 34688.
462 conjugacy classes of subgroups; only the 139 normal subgroups are shown.
This group has 462 conjugacy classes of subgroups — too many to draw. Only its 139 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. #31774604 | C2 | semidirect |
| 3. #31774244 | C2 | semidirect |
| 4. #31774216 | C2 | semidirect |
| 5. #31774188 | C2 | semidirect |
| 6. #31774126 | C2 | semidirect |
| 7. #31774098 | C2 | semidirect |
| 8. #31774050 | C2 | semidirect |
| 9. C4×#16864643 | C2 | semidirect |
| 10. C2×#22576082 | C2 | semidirect |
| 11. C8×D4×C271 | C2 | semidirect |
| 15. C2×#16864643 | C22 | semidirect |
| 16. #22576160 | C22 | semidirect |
| 19. #22576139 | C22 | semidirect |
| 24. C4×Dic542 | C22 | semidirect |
| 27. C2×C4⋊Dic271 | C22 | semidirect |
| 28. #22576092 | C22 | semidirect |
| 29. #22576092 | C22 | semidirect |
| 30. #22576085 | C22 | semidirect |
| 33. #22576082 | C22 | semidirect |
| 34. #22576082 | C22 | semidirect |
| 35. #22576082 | C22 | semidirect |
| 36. C22×C8×C271 | C22 | semidirect |
| 38. C4⋊C8×C271 | C22 | semidirect |
| 39. C22⋊C8×C271 | C22 | semidirect |
| 40. C4×C8×C271 | C22 | semidirect |
| 100. D4×C271 | SD16 | semidirect |
| 136. C271 | #3295 | semidirect |
| 147. C8×D4 | D271 | semidirect |
| 153. C22×C8 | C2×D271 | semidirect |
| 169. C4⋊C8 | C2×D271 | semidirect |
| 176. C22⋊C8 | C2×D271 | semidirect |
| 177. C4×C8 | C2×D271 | semidirect |
| 231. D4 | #16864643 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31774604 | 2 |
| D4×D1084 | 2 |
| #31774244 | 2 |
| #31774216 | 2 |
| #31774188 | 2 |
| #31774126 | 2 |
| #31774098 | 2 |
| #31774050 | 2 |
| C4×#16864643 | 2 |
| C2×#22576082 | 2 |
| C8×D4×C271 | 2 |
| #3295 | 271 |