Finite Group DatabasebetaFinite Group DatabasebetaOrder 17984.
218 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 218 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. #22582874 | C2 | semidirect |
| 2. #22582870 | C2 | semidirect |
| 3. #22582864 | C2 | semidirect |
| 4. #22582863 | C2 | semidirect |
| 5. #22582855 | C2 | semidirect |
| 7. #22582839 | C2 | semidirect |
| 8. C2×#17985117 | C2 | semidirect |
| 9. C22⋊Q8×C281 | C2 | semidirect |
| 66. C281 | #539 | semidirect |
| 73. C22⋊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 |
| #22582864 | 2 |
| #22582863 | 2 |
| #22582855 | 2 |
| #22582853 | 2 |
| #22582839 | 2 |
| C2×#17985117 | 2 |
| C22⋊Q8×C281 | 2 |
| #539 | 281 |