Finite Group DatabasebetaFinite Group DatabasebetaOrder 17792.
252 conjugacy classes of subgroups; only the 61 normal subgroups are shown.
This group has 252 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. #22580820 | C2 | semidirect |
| 4. #22580688 | C2 | semidirect |
| 5. #22580687 | C2 | semidirect |
| 6. #22580686 | C2 | semidirect |
| 7. #327×C139 | C2 | semidirect |
| 9. #17984841 | C4 | semidirect |
| 10. #17984838 | C4 | semidirect |
| 14. D4×Dic139 | C4 | semidirect |
| 15. #17984804 | C4 | semidirect |
| 118. C139 | #1514 | semidirect |
| 126. #327 | D139 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22581498 | 2 |
| #22581007 | 2 |
| #22580820 | 2 |
| #22580688 | 2 |
| #22580687 | 2 |
| #22580686 | 2 |
| #327×C139 | 2 |
| #1514 | 139 |