Finite Group DatabasebetaFinite Group DatabasebetaOrder 17792.
362 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 362 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. #22581682 | C2 | semidirect |
| 2. #22581348 | C2 | semidirect |
| 4. #22581172 | C2 | semidirect |
| 5. #22581163 | C2 | semidirect |
| 6. #22581158 | C2 | semidirect |
| 8. #22581084 | C2 | semidirect |
| 9. #22581053 | C2 | semidirect |
| 10. C4×#14555775 | C2 | semidirect |
| 121. C139 | #3400 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22581682 | 2 |
| #22581348 | 2 |
| #22581325 | 2 |
| #22581172 | 2 |
| #22581163 | 2 |
| #22581158 | 2 |
| #22581150 | 2 |
| #22581084 | 2 |
| #22581053 | 2 |
| C4×#14555775 | 2 |
| #559×C139 | 2 |
| #3400 | 139 |