Finite Group DatabasebetaFinite Group DatabasebetaOrder 17792.
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. #22581484 | C2 | semidirect |
| 2. C2×D4×Dic139 | C2 | semidirect |
| 3. #22581284 | C2 | semidirect |
| 4. #22581264 | C2 | semidirect |
| 5. #22581255 | C2 | semidirect |
| 6. #22581166 | C2 | semidirect |
| 7. #22581104 | C2 | semidirect |
| 8. #22581065 | C2 | semidirect |
| 9. #22581050 | C2 | semidirect |
| 10. #22581007 | C2 | semidirect |
| 15. #17984833 | C22 | semidirect |
| 16. #17984829 | C22 | semidirect |
| 19. #17984807 | C22 | semidirect |
| 25. D4×Dic139 | C22 | semidirect |
| 30. #17984775 | C22 | semidirect |
| 31. #17984774 | C22 | semidirect |
| 32. Dic139⋊C8 | C22 | semidirect |
| 33. #17984767 | C22 | semidirect |
| 35. #17984763 | C22 | semidirect |
| 37. #17984752 | C22 | semidirect |
| 140. C139 | #3114 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22581484 | 2 |
| C2×D4×Dic139 | 2 |
| #22581284 | 2 |
| #22581264 | 2 |
| #22581255 | 2 |
| #22581166 | 2 |
| #22581104 | 2 |
| #22581065 | 2 |
| #22581050 | 2 |
| #22581007 | 2 |
| #447×C139 | 2 |
| #3114 | 139 |