Finite Group DatabasebetaFinite Group DatabasebetaOrder 17792.
454 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 454 conjugacy classes of subgroups — too many to draw. Only its 125 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. #22581767 | C2 | semidirect |
| 2. #22581764 | C2 | semidirect |
| 3. #22581336 | C2 | semidirect |
| 4. #22581228 | C2 | semidirect |
| 5. #22581220 | C2 | semidirect |
| 6. #22581214 | C2 | semidirect |
| 7. #22581131 | C2 | semidirect |
| 8. #22581124 | C2 | semidirect |
| 9. #22581070 | C2 | semidirect |
| 10. #22581068 | C2 | semidirect |
| 11. #576×C139 | C2 | semidirect |
| 12. #17984889 | C22 | semidirect |
| 15. #17984872 | C22 | semidirect |
| 18. #17984868 | C22 | semidirect |
| 22. C2×Dic556 | C22 | semidirect |
| 25. C2×#14555773 | C22 | semidirect |
| 26. #17984849 | C22 | semidirect |
| 27. #17984848 | C22 | semidirect |
| 28. #17984829 | C22 | semidirect |
| 29. #17984778 | C22 | semidirect |
| 30. #17984777 | C22 | semidirect |
| 32. #17984769 | C22 | semidirect |
| 33. #17984768 | C22 | semidirect |
| 34. #17984760 | C22 | semidirect |
| 35. #17984759 | C22 | semidirect |
| 36. C8×Dic139 | C22 | semidirect |
| 149. C139 | #3290 | semidirect |
| 153. #576 | D139 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22581767 | 2 |
| #22581764 | 2 |
| #22581336 | 2 |
| #22581228 | 2 |
| #22581220 | 2 |
| #22581214 | 2 |
| #22581131 | 2 |
| #22581124 | 2 |
| #22581070 | 2 |
| #22581068 | 2 |
| #576×C139 | 2 |
| #3290 | 139 |