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. #22581751 | C2 | semidirect |
| 3. #22581524 | C2 | semidirect |
| 4. #22581134 | C2 | semidirect |
| 5. #22581124 | C2 | semidirect |
| 6. #22580970 | C2 | semidirect |
| 7. #22580969 | C2 | semidirect |
| 8. C2×#17984760 | C2 | semidirect |
| 9. #575×C139 | C2 | semidirect |
| 21. #17984873 | C22 | semidirect |
| 23. #17984868 | C22 | semidirect |
| 27. #17984840 | C22 | semidirect |
| 28. #17984829 | C22 | semidirect |
| 32. #17984769 | C22 | semidirect |
| 33. #17984768 | C22 | semidirect |
| 34. #17984760 | C22 | semidirect |
| 38. #137×C139 | C22 | semidirect |
| 40. AGL(1,ℤ/8)×C139 | C22 | semidirect |
| 185. C139 | #3020 | semidirect |
| 189. #575 | D139 | semidirect |
| 212. #137 | C2×D139 | semidirect |
| 216. AGL(1,ℤ/8) | 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 |
| #22581751 | 2 |
| #22581524 | 2 |
| #22581134 | 2 |
| #22581124 | 2 |
| #22580970 | 2 |
| #22580969 | 2 |
| C2×#17984760 | 2 |
| #575×C139 | 2 |
| #3020 | 139 |