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. #22581719 | C2 | semidirect |
| 4. #22581220 | C2 | semidirect |
| 5. #22581213 | C2 | semidirect |
| 6. #22581002 | C2 | semidirect |
| 7. #22580937 | C2 | semidirect |
| 8. C2×#17984759 | C2 | semidirect |
| 9. C2×AGL(1,ℤ/8)×C139 | C2 | semidirect |
| 11. #17984873 | C22 | semidirect |
| 15. #17984868 | C22 | semidirect |
| 21. #17984848 | C22 | semidirect |
| 26. #17984778 | C22 | semidirect |
| 27. #17984761 | C22 | semidirect |
| 28. #17984759 | C22 | semidirect |
| 29. #17984759 | C22 | semidirect |
| 34. C2×SD16×C139 | C22 | semidirect |
| 35. C2×D8×C139 | C22 | semidirect |
| 147. C139 | #3068 | semidirect |
| 151. C2×AGL(1,ℤ/8) | D139 | semidirect |
| 171. C2×SD16 | C2×D139 | semidirect |
| 173. C2×D8 | C2×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 |
| #22581719 | 2 |
| #22581220 | 2 |
| #22581213 | 2 |
| #22581002 | 2 |
| #22580937 | 2 |
| C2×#17984759 | 2 |
| C2×AGL(1,ℤ/8)×C139 | 2 |
| #3068 | 139 |