Finite Group DatabasebetaFinite Group DatabasebetaOrder 17792.
408 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 408 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. #22581482 | C2 | semidirect |
| 3. #22581359 | C2 | semidirect |
| 4. #22581343 | C2 | semidirect |
| 5. #22581318 | C2 | semidirect |
| 6. #22581205 | C2 | semidirect |
| 7. #22581202 | C2 | semidirect |
| 8. #22581038 | C2 | semidirect |
| 9. #22581033 | C2 | semidirect |
| 10. #22580905 | C2 | semidirect |
| 11. #489×C139 | C2 | semidirect |
| 100. C139⋊C8 | #41 | semidirect |
| 137. C139 | #3171 | semidirect |
| 144. #489 | D139 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22581504 | 2 |
| #22581482 | 2 |
| #22581359 | 2 |
| #22581343 | 2 |
| #22581318 | 2 |
| #22581205 | 2 |
| #22581202 | 2 |
| #22581038 | 2 |
| #22581033 | 2 |
| #22580905 | 2 |
| #489×C139 | 2 |
| #3171 | 139 |