Finite Group DatabasebetaFinite Group DatabasebetaOrder 17984.
196 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 196 conjugacy classes of subgroups — too many to draw. Only its 91 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. #22582878 | C2 | semidirect |
| 2. #22582877 | C2 | semidirect |
| 3. #22582874 | C2 | semidirect |
| 4. #22582874 | C2 | semidirect |
| 5. #22582872 | C2 | semidirect |
| 6. #22582872 | C2 | semidirect |
| 7. #22582870 | C2 | semidirect |
| 8. #22582869 | C2 | semidirect |
| 12. #22582858 | C2 | semidirect |
| 13. #22582857 | C2 | semidirect |
| 14. #22582855 | C2 | semidirect |
| 15. C22⋊Q8×C281 | C2 | semidirect |
| 97. C281 | #563 | semidirect |
| 113. C22⋊Q8 | D281 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22582878 | 2 |
| #22582877 | 2 |
| #22582874 | 2 |
| #22582872 | 2 |
| #22582870 | 2 |
| #22582869 | 2 |
| #22582865 | 2 |
| #22582862 | 2 |
| #22582861 | 2 |
| #22582858 | 2 |
| #22582857 | 2 |
| #22582855 | 2 |
| C22⋊Q8×C281 | 2 |
| #563 | 281 |