Finite Group DatabasebetaFinite Group DatabasebetaOrder 17792.
466 conjugacy classes of subgroups; only the 129 normal subgroups are shown.
This group has 466 conjugacy classes of subgroups — too many to draw. Only its 129 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. #22581753 | C2 | semidirect |
| 2. C2×#17984868 | C2 | semidirect |
| 3. C2×#17984868 | C2 | semidirect |
| 4. #22581719 | C2 | semidirect |
| 5. #22581222 | C2 | semidirect |
| 6. #22581215 | C2 | semidirect |
| 7. #22581001 | C2 | semidirect |
| 8. #22580935 | C2 | semidirect |
| 9. C2×#100×C139 | C2 | semidirect |
| 13. #17984875 | C22 | semidirect |
| 15. #17984870 | C22 | semidirect |
| 22. C2×#14555773 | C22 | semidirect |
| 24. C2×#14555770 | C22 | semidirect |
| 25. #17984850 | C22 | semidirect |
| 30. #17984777 | C22 | semidirect |
| 31. #17984760 | C22 | semidirect |
| 32. #17984758 | C22 | semidirect |
| 36. #100×C139 | C22 | semidirect |
| 147. C139 | #3068 | semidirect |
| 157. C2×#100 | D139 | semidirect |
| 184. #100 | C2×D139 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22581753 | 2 |
| C2×#17984868 | 2 |
| #22581719 | 2 |
| #22581222 | 2 |
| #22581215 | 2 |
| #22581001 | 2 |
| #22580935 | 2 |
| C2×#100×C139 | 2 |
| #3068 | 139 |