Finite Group DatabasebetaFinite Group DatabasebetaOrder 17792.
222 conjugacy classes of subgroups; only the 61 normal subgroups are shown.
This group has 222 conjugacy classes of subgroups — too many to draw. Only its 61 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 |
|---|---|---|
| 2. #22581007 | C2 | semidirect |
| 3. #22580817 | C2 | semidirect |
| 4. #22580691 | C2 | semidirect |
| 5. #22580689 | C2 | semidirect |
| 9. #17984833 | C4 | semidirect |
| 10. #17984829 | C4 | semidirect |
| 13. #17984807 | C4 | semidirect |
| 15. D4×Dic139 | C4 | semidirect |
| 108. C139 | #1512 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22581484 | 2 |
| #22581007 | 2 |
| #22580817 | 2 |
| #22580691 | 2 |
| #22580689 | 2 |
| #22580687 | 2 |
| #327×C139 | 2 |
| #1512 | 139 |