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. #31774428 | C2 | semidirect |
| 2. C2×D4×Dic271 | C2 | semidirect |
| 3. #31774228 | C2 | semidirect |
| 4. #31774208 | C2 | semidirect |
| 5. #31774199 | C2 | semidirect |
| 6. #31774110 | C2 | semidirect |
| 7. #31774048 | C2 | semidirect |
| 8. #31774009 | C2 | semidirect |
| 9. #31773994 | C2 | semidirect |
| 10. #31773951 | C2 | semidirect |
| 15. #22576151 | C22 | semidirect |
| 16. #22576147 | C22 | semidirect |
| 19. #22576125 | C22 | semidirect |
| 25. D4×Dic271 | C22 | semidirect |
| 30. #22576093 | C22 | semidirect |
| 31. #22576092 | C22 | semidirect |
| 32. Dic271⋊C8 | C22 | semidirect |
| 33. #22576085 | C22 | semidirect |
| 35. #22576081 | C22 | semidirect |
| 37. #22576070 | C22 | semidirect |
| 140. C271 | #3114 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31774428 | 2 |
| C2×D4×Dic271 | 2 |
| #31774228 | 2 |
| #31774208 | 2 |
| #31774199 | 2 |
| #31774110 | 2 |
| #31774048 | 2 |
| #31774009 | 2 |
| #31773994 | 2 |
| #31773951 | 2 |
| #447×C271 | 2 |
| #3114 | 271 |