Finite Group DatabasebetaFinite Group DatabasebetaOrder 17792.
466 conjugacy classes of subgroups; only the 145 normal subgroups are shown.
This group has 466 conjugacy classes of subgroups — too many to draw. Only its 145 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. #22581751 | C2 | semidirect |
| 2. C2×#17984870 | C2 | semidirect |
| 3. C2×#17984867 | C2 | semidirect |
| 4. #22581223 | C2 | semidirect |
| 5. #22581216 | C2 | semidirect |
| 6. #22581002 | C2 | semidirect |
| 7. #22580935 | C2 | semidirect |
| 8. C2×#17984758 | C2 | semidirect |
| 9. #568×C139 | C2 | semidirect |
| 13. #17984872 | C22 | semidirect |
| 19. #17984867 | C22 | semidirect |
| 21. C2×#14555774 | C22 | semidirect |
| 23. C2×D1112 | C22 | semidirect |
| 27. #17984778 | C22 | semidirect |
| 28. #17984760 | C22 | semidirect |
| 29. #17984758 | C22 | semidirect |
| 30. #17984758 | C22 | semidirect |
| 33. #131×C139 | C22 | semidirect |
| 147. C139 | #3068 | semidirect |
| 152. #568 | D139 | semidirect |
| 175. #131 | C2×D139 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22581751 | 2 |
| C2×#17984870 | 2 |
| C2×#17984867 | 2 |
| #22581223 | 2 |
| #22581216 | 2 |
| #22581002 | 2 |
| #22580935 | 2 |
| C2×#17984758 | 2 |
| #568×C139 | 2 |
| #3068 | 139 |