Finite Group DatabasebetaFinite Group DatabasebetaOrder 34688.
440 conjugacy classes of subgroups; only the 135 normal subgroups are shown.
This group has 440 conjugacy classes of subgroups — too many to draw. Only its 135 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. #31774450 | C2 | semidirect |
| 3. #31774200 | C2 | semidirect |
| 4. #31774196 | C2 | semidirect |
| 5. #31774186 | C2 | semidirect |
| 6. #31774176 | C2 | semidirect |
| 7. #31773937 | C2 | semidirect |
| 8. #31773920 | C2 | semidirect |
| 11. #428×C271 | C2 | semidirect |
| 15. #22576159 | C22 | semidirect |
| 16. #22576159 | C22 | semidirect |
| 17. #22576151 | C22 | semidirect |
| 18. #22576151 | C22 | semidirect |
| 30. #22576093 | C22 | semidirect |
| 31. #22576091 | C22 | semidirect |
| 32. Dic271⋊C8 | C22 | semidirect |
| 33. Dic271⋊C8 | C22 | semidirect |
| 41. #107×C271 | C22 | semidirect |
| 42. #106×C271 | C22 | semidirect |
| 48. C2×D1084 | Q8 | semidirect |
| 138. C271 | #3077 | semidirect |
| 147. #428 | D271 | semidirect |
| 173. #107 | C2×D271 | semidirect |
| 175. #106 | C2×D271 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31774450 | 2 |
| C2×#22576122 | 2 |
| #31774200 | 2 |
| #31774196 | 2 |
| #31774186 | 2 |
| #31774176 | 2 |
| #31773937 | 2 |
| #31773920 | 2 |
| #31773903 | 2 |
| #31773901 | 2 |
| #428×C271 | 2 |
| #3077 | 271 |