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. C2×#17984867 | C2 | semidirect |
| 2. C2×#17984867 | C2 | semidirect |
| 3. #22581720 | C2 | semidirect |
| 4. #22581221 | C2 | semidirect |
| 5. #22581218 | C2 | semidirect |
| 6. #22581001 | C2 | semidirect |
| 7. #22580937 | C2 | semidirect |
| 8. C2×#17984758 | C2 | semidirect |
| 9. #575×C139 | C2 | semidirect |
| 16. C2×#14555772 | C22 | semidirect |
| 18. C2×#14555770 | C22 | semidirect |
| 20. #17984849 | C22 | semidirect |
| 25. #17984777 | C22 | semidirect |
| 26. #17984761 | C22 | semidirect |
| 27. #17984759 | C22 | semidirect |
| 28. #17984758 | C22 | semidirect |
| 32. #137×C139 | C22 | semidirect |
| 34. AGL(1,ℤ/8)×C139 | C22 | semidirect |
| 147. C139 | #3068 | semidirect |
| 149. #575 | D139 | semidirect |
| 162. #137 | C2×D139 | semidirect |
| 168. 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×#17984867 | 2 |
| #22581720 | 2 |
| #22581221 | 2 |
| #22581218 | 2 |
| #22581001 | 2 |
| #22580937 | 2 |
| C2×#17984758 | 2 |
| #575×C139 | 2 |
| #3068 | 139 |