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. #31774378 | C2 | semidirect |
| 3. #31774224 | C2 | semidirect |
| 4. #31774223 | C2 | semidirect |
| 5. #31774217 | C2 | semidirect |
| 6. #31774212 | C2 | semidirect |
| 7. #31773933 | C2 | semidirect |
| 8. #31773903 | C2 | semidirect |
| 9. C2×#22576080 | C2 | semidirect |
| 10. #31773865 | C2 | semidirect |
| 11. #428×C271 | C2 | semidirect |
| 24. #22576118 | C22 | semidirect |
| 25. C4⋊C4×D271 | C22 | semidirect |
| 26. #22576093 | C22 | semidirect |
| 27. #22576093 | C22 | semidirect |
| 28. #22576091 | C22 | semidirect |
| 29. #22576091 | C22 | semidirect |
| 34. (C2×D271)⋊C8 | C22 | semidirect |
| 35. (C2×D271)⋊C8 | C22 | semidirect |
| 39. #107×C271 | C22 | semidirect |
| 40. #106×C271 | C22 | semidirect |
| 134. C271 | #3096 | semidirect |
| 142. #428 | D271 | semidirect |
| 166. #107 | C2×D271 | semidirect |
| 169. #106 | C2×D271 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31774466 | 2 |
| #31774378 | 2 |
| #31774224 | 2 |
| #31774223 | 2 |
| #31774217 | 2 |
| #31774212 | 2 |
| #31773933 | 2 |
| #31773903 | 2 |
| C2×#22576080 | 2 |
| #31773865 | 2 |
| #428×C271 | 2 |
| #3096 | 271 |