Finite Group DatabasebetaFinite Group DatabasebetaOrder 17984.
234 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 234 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 |
|---|---|---|
| 1. #22582873 | C2 | semidirect |
| 2. #22582871 | C2 | semidirect |
| 3. #22582867 | C2 | semidirect |
| 4. #22582862 | C2 | semidirect |
| 5. #22582858 | C2 | semidirect |
| 7. C4×Dic562 | C2 | semidirect |
| 8. C4×D1124 | C2 | semidirect |
| 9. C4×C22⋊D281 | C2 | semidirect |
| 10. #22582836 | C2 | semidirect |
| 11. C2×C42×C281 | C2 | semidirect |
| 74. C281 | #529 | semidirect |
| 86. C2×C42 | D281 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22582873 | 2 |
| #22582871 | 2 |
| #22582867 | 2 |
| #22582862 | 2 |
| #22582858 | 2 |
| #22582853 | 2 |
| C4×Dic562 | 2 |
| C4×D1124 | 2 |
| C4×C22⋊D281 | 2 |
| #22582836 | 2 |
| C2×C42×C281 | 2 |
| #529 | 281 |