Finite Group DatabasebetaFinite Group DatabasebetaOrder 17984.
216 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 216 conjugacy classes of subgroups — too many to draw. Only its 95 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. #22582874 | C2 | semidirect |
| 3. #22582868 | C2 | semidirect |
| 4. #22582865 | C2 | semidirect |
| 5. #22582861 | C2 | semidirect |
| 6. #22582859 | C2 | semidirect |
| 8. Q8×Dic281 | C2 | semidirect |
| 9. #22582841 | C2 | semidirect |
| 10. #22582838 | C2 | semidirect |
| 11. C22⋊Q8×C281 | C2 | semidirect |
| 73. C281 | #542 | semidirect |
| 81. 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 |
| #22582874 | 2 |
| #22582868 | 2 |
| #22582865 | 2 |
| #22582861 | 2 |
| #22582859 | 2 |
| #22582853 | 2 |
| Q8×Dic281 | 2 |
| #22582841 | 2 |
| #22582838 | 2 |
| C22⋊Q8×C281 | 2 |
| #542 | 281 |