Finite Group DatabasebetaFinite Group DatabasebetaOrder 17792.
784 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 784 conjugacy classes of subgroups — too many to draw. Only its 149 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. C2×#17984888 | C2 | semidirect |
| 2. C2×#17984867 | C2 | semidirect |
| 3. C22×D1112 | C2 | semidirect |
| 4. #22581522 | C2 | semidirect |
| 5. #22581101 | C2 | semidirect |
| 6. #22581088 | C2 | semidirect |
| 7. #22580957 | C2 | semidirect |
| 8. #22580919 | C2 | semidirect |
| 9. #416×C139 | C2 | semidirect |
| 12. C2×#14555786 | C22 | semidirect |
| 17. C22×D556 | C22 | semidirect |
| 19. C2×D4×D139 | C22 | semidirect |
| 21. C2×#14555772 | C22 | semidirect |
| 23. C2×D1112 | C22 | semidirect |
| 24. C2×#14555770 | C22 | semidirect |
| 25. C2×#14555769 | C22 | semidirect |
| 28. #17984817 | C22 | semidirect |
| 30. #17984762 | C22 | semidirect |
| 31. (C2×D139)⋊C8 | C22 | semidirect |
| 33. C22×C8×C139 | C22 | semidirect |
| 34. #117×C139 | C22 | semidirect |
| 35. #103×C139 | C22 | semidirect |
| 36. #102×C139 | C22 | semidirect |
| 55. C2×D556 | D4 | semidirect |
| 72. #41×C139 | D4 | semidirect |
| 151. C139 | #3008 | semidirect |
| 160. #416 | D139 | semidirect |
| 179. C22×C8 | C2×D139 | semidirect |
| 184. #117 | C2×D139 | semidirect |
| 185. #103 | C2×D139 | semidirect |
| 187. #102 | C2×D139 | semidirect |
| 198. #41 | D556 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17984888 | 2 |
| C2×#17984867 | 2 |
| C22×D1112 | 2 |
| #22581522 | 2 |
| #22581101 | 2 |
| #22581088 | 2 |
| #22580957 | 2 |
| #22580919 | 2 |
| #416×C139 | 2 |
| #3008 | 139 |