Finite Group DatabasebetaFinite Group DatabasebetaOrder 17792.
396 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 396 conjugacy classes of subgroups — too many to draw. Only its 123 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. #22581663 | C2 | semidirect |
| 2. #22581625 | C2 | semidirect |
| 3. #22581318 | C2 | semidirect |
| 4. #22581300 | C2 | semidirect |
| 5. #22581254 | C2 | semidirect |
| 6. #22581244 | C2 | semidirect |
| 7. #22581149 | C2 | semidirect |
| 8. #22581149 | C2 | semidirect |
| 9. #22581066 | C2 | semidirect |
| 10. C4×D1112 | C2 | semidirect |
| 11. #446×C139 | C2 | semidirect |
| 87. D556 | #41 | semidirect |
| 129. C139 | #3366 | semidirect |
| 139. #446 | D139 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22581663 | 2 |
| #22581625 | 2 |
| #22581318 | 2 |
| #22581300 | 2 |
| #22581254 | 2 |
| #22581244 | 2 |
| #22581149 | 2 |
| #22581066 | 2 |
| C4×D1112 | 2 |
| #446×C139 | 2 |
| #3366 | 139 |