Finite Group DatabasebetaFinite Group DatabasebetaOrder 34688.
448 conjugacy classes of subgroups; only the 129 normal subgroups are shown.
This group has 448 conjugacy classes of subgroups — too many to draw. Only its 129 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. #31774449 | C2 | semidirect |
| 3. #31774228 | C2 | semidirect |
| 4. #31774225 | C2 | semidirect |
| 5. #31774185 | C2 | semidirect |
| 6. #31774100 | C2 | semidirect |
| 8. #31773988 | C2 | semidirect |
| 9. SD16×Dic271 | C2 | semidirect |
| 10. #31773947 | C2 | semidirect |
| 14. #22576159 | C22 | semidirect |
| 15. #22576158 | C22 | semidirect |
| 19. Q8×Dic271 | C22 | semidirect |
| 21. #22576125 | C22 | semidirect |
| 30. #22576092 | C22 | semidirect |
| 31. #22576091 | C22 | semidirect |
| 32. Dic271⋊C8 | C22 | semidirect |
| 33. #22576085 | C22 | semidirect |
| 34. #22576084 | C22 | semidirect |
| 37. C8×Dic271 | C22 | semidirect |
| 91. C2×Dic271 | SD16 | semidirect |
| 136. C271 | #3101 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31774449 | 2 |
| C2×D4×Dic271 | 2 |
| #31774228 | 2 |
| #31774225 | 2 |
| #31774185 | 2 |
| #31774100 | 2 |
| #31774048 | 2 |
| #31773988 | 2 |
| SD16×Dic271 | 2 |
| #31773947 | 2 |
| #450×C271 | 2 |
| #3101 | 271 |