Finite Group DatabasebetaFinite Group DatabasebetaOrder 17984.
124 conjugacy classes of subgroups; only the 45 normal subgroups are shown.
This group has 124 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 |
|---|---|---|
| 1. C2×#17985126 | C2 | semidirect |
| 2. C22×#14555886 | C2 | semidirect |
| 3. #22582858 | C2 | semidirect |
| 4. #22582810 | C2 | semidirect |
| 5. #22582802 | C2 | semidirect |
| 6. #22582800 | C2 | semidirect |
| 26. #14555886 | D4 | semidirect |
| 42. C22×C281 | SD16 | semidirect |
| 55. C281 | #465 | semidirect |
| 98. C22 | #17985126 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17985126 | 2 |
| C22×#14555886 | 2 |
| #22582858 | 2 |
| #22582810 | 2 |
| #22582802 | 2 |
| #22582800 | 2 |
| #121×C281 | 2 |
| #465 | 281 |