Finite Group DatabasebetaFinite Group DatabasebetaOrder 17984.
234 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 234 conjugacy classes of subgroups — too many to draw. Only its 101 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. #22582874 | C2 | semidirect |
| 2. #22582870 | C2 | semidirect |
| 3. #22582868 | C2 | semidirect |
| 4. #22582864 | C2 | semidirect |
| 5. #22582855 | C2 | semidirect |
| 7. C4×D1124 | C2 | semidirect |
| 8. C4×D1124 | C2 | semidirect |
| 9. #22582836 | C2 | semidirect |
| 10. C42×D281 | C2 | semidirect |
| 11. C4×Q8×C281 | C2 | semidirect |
| 74. C281 | #529 | semidirect |
| 82. C4×Q8 | D281 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22582874 | 2 |
| #22582870 | 2 |
| #22582868 | 2 |
| #22582864 | 2 |
| #22582855 | 2 |
| #22582854 | 2 |
| C4×D1124 | 2 |
| #22582836 | 2 |
| C42×D281 | 2 |
| C4×Q8×C281 | 2 |
| #529 | 281 |