Finite Group DatabasebetaFinite Group DatabasebetaOrder 34688.
398 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 398 conjugacy classes of subgroups — too many to draw. Only its 141 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. #31774199 | C2 | semidirect |
| 4. #31774195 | C2 | semidirect |
| 5. #31774185 | C2 | semidirect |
| 6. #31774175 | C2 | semidirect |
| 7. #31773937 | C2 | semidirect |
| 8. #31773935 | C2 | semidirect |
| 9. #31773923 | C2 | semidirect |
| 14. #22576159 | C22 | semidirect |
| 16. #22576151 | C22 | semidirect |
| 26. #22576094 | C22 | semidirect |
| 27. #22576094 | C22 | semidirect |
| 28. #22576093 | C22 | semidirect |
| 29. #22576092 | C22 | semidirect |
| 30. #22576092 | C22 | semidirect |
| 31. #22576091 | C22 | semidirect |
| 32. Dic271⋊C8 | C22 | semidirect |
| 33. Dic271⋊C8 | C22 | semidirect |
| 66. C2×D4×C271 | Q8 | semidirect |
| 124. C271 | #3081 | semidirect |
| 170. C2×D4 | Dic542 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31774528 | 2 |
| #31774372 | 2 |
| #31774199 | 2 |
| #31774195 | 2 |
| #31774185 | 2 |
| #31774175 | 2 |
| #31773937 | 2 |
| #31773935 | 2 |
| #31773923 | 2 |
| #31773902 | 2 |
| C2×#102×C271 | 2 |
| #3081 | 271 |