Finite Group DatabasebetaFinite Group DatabasebetaOrder 17792.
356 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 356 conjugacy classes of subgroups — too many to draw. Only its 113 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. #22581672 | C2 | semidirect |
| 2. #22581344 | C2 | semidirect |
| 3. #22581172 | C2 | semidirect |
| 5. #22581161 | C2 | semidirect |
| 6. #22581083 | C2 | semidirect |
| 7. #22581054 | C2 | semidirect |
| 8. C4×Dic556 | C2 | semidirect |
| 102. C139 | #3402 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22581672 | 2 |
| #22581344 | 2 |
| #22581172 | 2 |
| #22581166 | 2 |
| #22581161 | 2 |
| #22581083 | 2 |
| #22581054 | 2 |
| C4×Dic556 | 2 |
| #495×C139 | 2 |
| #3402 | 139 |