Finite Group DatabasebetaFinite Group DatabasebetaOrder 17792.
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. #22581489 | C2 | semidirect |
| 2. C2×#17984804 | C2 | semidirect |
| 3. #22581266 | C2 | semidirect |
| 4. #22581252 | C2 | semidirect |
| 5. #22581171 | C2 | semidirect |
| 6. #22581103 | C2 | semidirect |
| 8. #22581064 | C2 | semidirect |
| 9. #22581056 | C2 | semidirect |
| 10. #22581007 | C2 | semidirect |
| 11. #483×C139 | C2 | semidirect |
| 17. #17984833 | C22 | semidirect |
| 18. #17984831 | C22 | semidirect |
| 21. Q8×Dic139 | C22 | semidirect |
| 26. #17984804 | C22 | semidirect |
| 31. #17984775 | C22 | semidirect |
| 32. Dic139⋊C8 | C22 | semidirect |
| 35. #17984762 | C22 | semidirect |
| 37. #17984752 | C22 | semidirect |
| 40. #106×C139 | C22 | semidirect |
| 41. #103×C139 | C22 | semidirect |
| 140. C139 | #3114 | semidirect |
| 144. #483 | D139 | semidirect |
| 175. #106 | C2×D139 | semidirect |
| 177. #103 | C2×D139 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22581489 | 2 |
| C2×#17984804 | 2 |
| #22581266 | 2 |
| #22581252 | 2 |
| #22581171 | 2 |
| #22581103 | 2 |
| #22581089 | 2 |
| #22581064 | 2 |
| #22581056 | 2 |
| #22581007 | 2 |
| #483×C139 | 2 |
| #3114 | 139 |