Finite Group DatabasebetaFinite Group DatabasebetaOrder 17792.
380 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 380 conjugacy classes of subgroups — too many to draw. Only its 121 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. #22581688 | C2 | semidirect |
| 2. #22581342 | C2 | semidirect |
| 3. #22581337 | C2 | semidirect |
| 4. #22581176 | C2 | semidirect |
| 5. #22581169 | C2 | semidirect |
| 6. #22581149 | C2 | semidirect |
| 7. #22581055 | C2 | semidirect |
| 8. C4×D1112 | C2 | semidirect |
| 9. #446×C139 | C2 | semidirect |
| 108. C139 | #3403 | semidirect |
| 116. #446 | D139 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22581688 | 2 |
| #22581342 | 2 |
| #22581337 | 2 |
| #22581176 | 2 |
| #22581169 | 2 |
| #22581149 | 2 |
| #22581055 | 2 |
| C4×D1112 | 2 |
| #446×C139 | 2 |
| #3403 | 139 |