Finite Group DatabasebetaFinite Group DatabasebetaOrder 34688.
404 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 404 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 |
|---|---|---|
| 1. #31774528 | C2 | semidirect |
| 3. #31774260 | C2 | semidirect |
| 4. #31774258 | C2 | semidirect |
| 5. #31774253 | C2 | semidirect |
| 6. #31774242 | C2 | semidirect |
| 7. #31773903 | C2 | semidirect |
| 8. #31773893 | C2 | semidirect |
| 9. C2×#22576080 | C2 | semidirect |
| 10. #31773855 | C2 | semidirect |
| 11. #417×C271 | C2 | semidirect |
| 15. #22576159 | C22 | semidirect |
| 18. #22576151 | C22 | semidirect |
| 26. #22576084 | C22 | semidirect |
| 27. #22576084 | C22 | semidirect |
| 30. #22576081 | C22 | semidirect |
| 31. #22576081 | C22 | semidirect |
| 34. #22576070 | C22 | semidirect |
| 35. C8×Dic271 | C22 | semidirect |
| 39. #103×C271 | C22 | semidirect |
| 40. #102×C271 | C22 | semidirect |
| 135. C271 | #3136 | semidirect |
| 144. #417 | D271 | semidirect |
| 167. #103 | C2×D271 | semidirect |
| 174. #102 | C2×D271 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31774528 | 2 |
| #31774461 | 2 |
| #31774260 | 2 |
| #31774258 | 2 |
| #31774253 | 2 |
| #31774242 | 2 |
| #31773903 | 2 |
| #31773893 | 2 |
| C2×#22576080 | 2 |
| #31773855 | 2 |
| #417×C271 | 2 |
| #3136 | 271 |