Finite Group DatabasebetaFinite Group DatabasebetaOrder 17984.
106 conjugacy classes of subgroups; only the 45 normal subgroups are shown.
This group has 106 conjugacy classes of subgroups — too many to draw. Only its 45 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. #22582887 | C2 | semidirect |
| 3. #22582886 | C2 | semidirect |
| 4. #22582814 | C2 | semidirect |
| 5. #22582807 | C2 | semidirect |
| 6. C4×#14555886 | C2 | semidirect |
| 7. #104×C281 | C2 | semidirect |
| 9. #17985128 | C4 | semidirect |
| 10. #17985126 | C4 | semidirect |
| 11. #17985125 | C4 | semidirect |
| 12. #17985123 | C4 | semidirect |
| 51. C281 | #443 | semidirect |
| 58. #104 | D281 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22582899 | 2 |
| #22582887 | 2 |
| #22582886 | 2 |
| #22582814 | 2 |
| #22582807 | 2 |
| C4×#14555886 | 2 |
| #104×C281 | 2 |
| #443 | 281 |