Finite Group DatabasebetaFinite Group DatabasebetaOrder 34688.
450 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 450 conjugacy classes of subgroups — too many to draw. Only its 121 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. #31774433 | C2 | semidirect |
| 2. C2×D4×Dic271 | C2 | semidirect |
| 3. #31774225 | C2 | semidirect |
| 4. #31774211 | C2 | semidirect |
| 5. #31774195 | C2 | semidirect |
| 6. #31774114 | C2 | semidirect |
| 8. #31774006 | C2 | semidirect |
| 9. #31773998 | C2 | semidirect |
| 10. #31773951 | C2 | semidirect |
| 11. #450×C271 | C2 | semidirect |
| 15. #22576151 | C22 | semidirect |
| 16. #22576149 | C22 | semidirect |
| 19. Q8×Dic271 | C22 | semidirect |
| 24. #22576122 | C22 | semidirect |
| 30. #22576094 | C22 | semidirect |
| 31. #22576091 | C22 | semidirect |
| 32. Dic271⋊C8 | C22 | semidirect |
| 33. #22576084 | C22 | semidirect |
| 34. #22576082 | C22 | semidirect |
| 37. #22576070 | C22 | semidirect |
| 140. C271 | #3114 | semidirect |
| 148. #450 | D271 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31774433 | 2 |
| C2×D4×Dic271 | 2 |
| #31774225 | 2 |
| #31774211 | 2 |
| #31774195 | 2 |
| #31774114 | 2 |
| #31774031 | 2 |
| #31774006 | 2 |
| #31773998 | 2 |
| #31773951 | 2 |
| #450×C271 | 2 |
| #3114 | 271 |