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. #22581489 | C2 | semidirect |
| 2. C2×D4×Dic139 | C2 | semidirect |
| 3. #22581281 | C2 | semidirect |
| 4. #22581267 | C2 | semidirect |
| 5. #22581251 | C2 | semidirect |
| 6. #22581170 | C2 | semidirect |
| 8. #22581062 | C2 | semidirect |
| 9. #22581054 | C2 | semidirect |
| 10. #22581007 | C2 | semidirect |
| 11. #450×C139 | C2 | semidirect |
| 15. #17984833 | C22 | semidirect |
| 16. #17984831 | C22 | semidirect |
| 19. Q8×Dic139 | C22 | semidirect |
| 24. #17984804 | C22 | semidirect |
| 30. #17984776 | C22 | semidirect |
| 31. #17984773 | C22 | semidirect |
| 32. Dic139⋊C8 | C22 | semidirect |
| 33. #17984766 | C22 | semidirect |
| 34. #17984764 | C22 | semidirect |
| 37. #17984752 | C22 | semidirect |
| 140. C139 | #3114 | semidirect |
| 148. #450 | D139 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22581489 | 2 |
| C2×D4×Dic139 | 2 |
| #22581281 | 2 |
| #22581267 | 2 |
| #22581251 | 2 |
| #22581170 | 2 |
| #22581087 | 2 |
| #22581062 | 2 |
| #22581054 | 2 |
| #22581007 | 2 |
| #450×C139 | 2 |
| #3114 | 139 |