Finite Group DatabasebetaFinite Group DatabasebetaOrder 17792.
466 conjugacy classes of subgroups; only the 137 normal subgroups are shown.
This group has 466 conjugacy classes of subgroups — too many to draw. Only its 137 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×#17984868 | C2 | semidirect |
| 3. #22581720 | C2 | semidirect |
| 4. #22581221 | C2 | semidirect |
| 5. #22581214 | C2 | semidirect |
| 6. #22581001 | C2 | semidirect |
| 7. #22580935 | C2 | semidirect |
| 8. C2×#17984759 | C2 | semidirect |
| 9. C2×AGL(1,ℤ/8)×C139 | C2 | semidirect |
| 12. #17984872 | C22 | semidirect |
| 16. #17984867 | C22 | semidirect |
| 18. C2×#14555773 | C22 | semidirect |
| 19. C2×#14555770 | C22 | semidirect |
| 21. #17984849 | C22 | semidirect |
| 26. #17984777 | C22 | semidirect |
| 27. #17984760 | C22 | semidirect |
| 28. #17984759 | C22 | semidirect |
| 29. #17984758 | C22 | semidirect |
| 147. C139 | #3068 | semidirect |
| 151. C2×AGL(1,ℤ/8) | D139 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22581751 | 2 |
| C2×#17984868 | 2 |
| #22581720 | 2 |
| #22581221 | 2 |
| #22581214 | 2 |
| #22581001 | 2 |
| #22580935 | 2 |
| C2×#17984759 | 2 |
| C2×AGL(1,ℤ/8)×C139 | 2 |
| #3068 | 139 |