Finite Group DatabasebetaFinite Group DatabasebetaOrder 17984.
270 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 270 conjugacy classes of subgroups — too many to draw. Only its 103 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. C2×Q8×D281 | C2 | semidirect |
| 3. #22582878 | C2 | semidirect |
| 4. #22582865 | C2 | semidirect |
| 5. #22582864 | C2 | semidirect |
| 6. #22582861 | C2 | semidirect |
| 7. #22582859 | C2 | semidirect |
| 8. #22582858 | C2 | semidirect |
| 9. #22582855 | C2 | semidirect |
| 10. #22582837 | C2 | semidirect |
| 11. C22⋊Q8×C281 | C2 | semidirect |
| 83. C281 | #536 | semidirect |
| 94. C22⋊Q8 | D281 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17985138 | 2 |
| C2×Q8×D281 | 2 |
| #22582878 | 2 |
| #22582865 | 2 |
| #22582864 | 2 |
| #22582861 | 2 |
| #22582859 | 2 |
| #22582858 | 2 |
| #22582855 | 2 |
| #22582837 | 2 |
| C22⋊Q8×C281 | 2 |
| #536 | 281 |