Finite Group DatabasebetaFinite Group DatabasebetaOrder 17792.
380 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 380 conjugacy classes of subgroups — too many to draw. Only its 121 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. #22581484 | C2 | semidirect |
| 2. #22581354 | C2 | semidirect |
| 3. #22581336 | C2 | semidirect |
| 4. #22581306 | C2 | semidirect |
| 5. #22581194 | C2 | semidirect |
| 6. #22581180 | C2 | semidirect |
| 7. #22581047 | C2 | semidirect |
| 8. #22581044 | C2 | semidirect |
| 9. D8×Dic139 | C2 | semidirect |
| 10. C2×C8×Dic139 | C2 | semidirect |
| 118. C139 | #3168 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22581484 | 2 |
| #22581354 | 2 |
| #22581336 | 2 |
| #22581306 | 2 |
| #22581194 | 2 |
| #22581180 | 2 |
| #22581047 | 2 |
| #22581044 | 2 |
| D8×Dic139 | 2 |
| C2×C8×Dic139 | 2 |
| #466×C139 | 2 |
| #3168 | 139 |