Finite Group DatabasebetaFinite Group DatabasebetaOrder 17792.
698 conjugacy classes of subgroups; only the 145 normal subgroups are shown.
This group has 698 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. C2×#17984889 | C2 | semidirect |
| 2. #22581753 | C2 | semidirect |
| 3. #22581751 | C2 | semidirect |
| 4. #22581529 | C2 | semidirect |
| 5. #22581137 | C2 | semidirect |
| 6. #22581127 | C2 | semidirect |
| 7. #22580971 | C2 | semidirect |
| 8. C2×#17984760 | C2 | semidirect |
| 9. #421×C139 | C2 | semidirect |
| 23. #17984875 | C22 | semidirect |
| 25. #17984872 | C22 | semidirect |
| 27. #17984870 | C22 | semidirect |
| 29. #17984867 | C22 | semidirect |
| 33. #17984842 | C22 | semidirect |
| 34. #17984830 | C22 | semidirect |
| 37. #17984770 | C22 | semidirect |
| 38. #17984760 | C22 | semidirect |
| 42. #104×C139 | C22 | semidirect |
| 185. C139 | #3020 | semidirect |
| 194. #421 | D139 | semidirect |
| 227. #104 | C2×D139 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17984889 | 2 |
| #22581753 | 2 |
| #22581751 | 2 |
| #22581529 | 2 |
| #22581137 | 2 |
| #22581127 | 2 |
| #22580971 | 2 |
| C2×#17984760 | 2 |
| #421×C139 | 2 |
| #3020 | 139 |