Finite Group DatabasebetaFinite Group DatabasebetaOrder 34688.
418 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 418 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 |
|---|---|---|
| 2. #31774377 | C2 | semidirect |
| 3. #31774220 | C2 | semidirect |
| 4. #31774219 | C2 | semidirect |
| 5. #31774214 | C2 | semidirect |
| 6. #31774209 | C2 | semidirect |
| 7. #31773939 | C2 | semidirect |
| 8. #31773933 | C2 | semidirect |
| 9. C2×#22576081 | C2 | semidirect |
| 10. #31773865 | C2 | semidirect |
| 11. #418×C271 | C2 | semidirect |
| 23. #22576118 | C22 | semidirect |
| 25. C4⋊C4×D271 | C22 | semidirect |
| 26. #22576094 | C22 | semidirect |
| 27. #22576093 | C22 | semidirect |
| 28. #22576093 | C22 | semidirect |
| 29. #22576092 | C22 | semidirect |
| 30. #22576091 | C22 | semidirect |
| 31. #22576091 | C22 | semidirect |
| 34. (C2×D271)⋊C8 | C22 | semidirect |
| 35. (C2×D271)⋊C8 | C22 | semidirect |
| 134. C271 | #3096 | semidirect |
| 144. #418 | D271 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31774464 | 2 |
| #31774377 | 2 |
| #31774220 | 2 |
| #31774219 | 2 |
| #31774214 | 2 |
| #31774209 | 2 |
| #31773939 | 2 |
| #31773933 | 2 |
| C2×#22576081 | 2 |
| #31773865 | 2 |
| #418×C271 | 2 |
| #3096 | 271 |