Finite Group DatabasebetaFinite Group DatabasebetaOrder 17792.
398 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 398 conjugacy classes of subgroups — too many to draw. Only its 133 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. #22581584 | C2 | semidirect |
| 3. #22581256 | C2 | semidirect |
| 4. #22581252 | C2 | semidirect |
| 5. #22581242 | C2 | semidirect |
| 6. #22581232 | C2 | semidirect |
| 7. #22580989 | C2 | semidirect |
| 8. #22580981 | C2 | semidirect |
| 11. #428×C139 | C2 | semidirect |
| 15. #17984841 | C22 | semidirect |
| 17. #17984833 | C22 | semidirect |
| 26. #17984775 | C22 | semidirect |
| 27. #17984775 | C22 | semidirect |
| 28. #17984773 | C22 | semidirect |
| 29. #17984773 | C22 | semidirect |
| 30. Dic139⋊C8 | C22 | semidirect |
| 31. Dic139⋊C8 | C22 | semidirect |
| 39. #107×C139 | C22 | semidirect |
| 40. #106×C139 | C22 | semidirect |
| 45. C2×D556 | Q8 | semidirect |
| 124. C139 | #3081 | semidirect |
| 132. #428 | D139 | semidirect |
| 156. #107 | C2×D139 | semidirect |
| 159. #106 | C2×D139 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22581584 | 2 |
| #22581427 | 2 |
| #22581256 | 2 |
| #22581252 | 2 |
| #22581242 | 2 |
| #22581232 | 2 |
| #22580989 | 2 |
| #22580981 | 2 |
| #22580959 | 2 |
| C2×#17984762 | 2 |
| #428×C139 | 2 |
| #3081 | 139 |