Finite Group DatabasebetaFinite Group DatabasebetaOrder 34688.
450 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 450 conjugacy classes of subgroups — too many to draw. Only its 117 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. #31774428 | C2 | semidirect |
| 2. C2×#22576122 | C2 | semidirect |
| 3. #31774227 | C2 | semidirect |
| 4. #31774200 | C2 | semidirect |
| 5. #31774111 | C2 | semidirect |
| 6. #31774050 | C2 | semidirect |
| 8. #31774006 | C2 | semidirect |
| 9. #31773996 | C2 | semidirect |
| 10. #31773951 | C2 | semidirect |
| 11. #480×C271 | C2 | semidirect |
| 17. #22576151 | C22 | semidirect |
| 18. #22576147 | C22 | semidirect |
| 21. #22576125 | C22 | semidirect |
| 23. D4×Dic271 | C22 | semidirect |
| 31. #22576091 | C22 | semidirect |
| 32. Dic271⋊C8 | C22 | semidirect |
| 33. #22576083 | C22 | semidirect |
| 37. #22576070 | C22 | semidirect |
| 40. #107×C271 | C22 | semidirect |
| 41. #102×C271 | C22 | semidirect |
| 140. C271 | #3114 | semidirect |
| 145. #480 | D271 | semidirect |
| 174. #107 | C2×D271 | semidirect |
| 180. #102 | C2×D271 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31774428 | 2 |
| C2×#22576122 | 2 |
| #31774227 | 2 |
| #31774200 | 2 |
| #31774111 | 2 |
| #31774050 | 2 |
| #31774030 | 2 |
| #31774006 | 2 |
| #31773996 | 2 |
| #31773951 | 2 |
| #480×C271 | 2 |
| #3114 | 271 |