Finite Group DatabasebetaFinite Group DatabasebetaOrder 17792.
430 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 430 conjugacy classes of subgroups — too many to draw. Only its 115 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. #22581504 | C2 | semidirect |
| 2. #22581500 | C2 | semidirect |
| 3. #22581242 | C2 | semidirect |
| 4. #22581240 | C2 | semidirect |
| 5. #22581207 | C2 | semidirect |
| 6. #22581205 | C2 | semidirect |
| 7. #22581149 | C2 | semidirect |
| 8. #22581148 | C2 | semidirect |
| 9. #22581147 | C2 | semidirect |
| 10. #22580975 | C2 | semidirect |
| 11. #476×C139 | C2 | semidirect |
| 150. C139 | #3253 | semidirect |
| 156. #476 | D139 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22581504 | 2 |
| #22581500 | 2 |
| #22581242 | 2 |
| #22581240 | 2 |
| #22581207 | 2 |
| #22581205 | 2 |
| #22581149 | 2 |
| #22581148 | 2 |
| #22581147 | 2 |
| #22580975 | 2 |
| #476×C139 | 2 |
| #3253 | 139 |