Finite Group DatabasebetaFinite Group DatabasebetaOrder 17984.
196 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 196 conjugacy classes of subgroups — too many to draw. Only its 91 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C23×D281 |
| commutator, socle, cosocle | C22×C281 | C24 |
| Fitting | #126×C281 | C2 |
| prime radical | C2×C22⋊D281 | C22 |
| hypercenter | #126 | D281 |
| hypocenter | C281 | #563 |
| LCS | G ▷ C22×C281 ▷ C281 | |
| UCS | C1 ◁ C22 ◁ #126 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #22582879 | C2 | semidirect |
| 2. #22582878 | C2 | semidirect |
| 3. #22582874 | C2 | semidirect |
| 4. #22582873 | C2 | semidirect |
| 5. #22582872 | C2 | semidirect |
| 6. #22582870 | C2 | semidirect |
| 7. #22582869 | C2 | semidirect |
| 11. #22582859 | C2 | semidirect |
| 12. #22582857 | C2 | semidirect |
| 13. #22582856 | C2 | semidirect |
| 14. #22582856 | C2 | semidirect |
| 15. #126×C281 | C2 | semidirect |
| 97. C281 | #563 | semidirect |
| 104. #126 | D281 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22582879 | 2 |
| #22582878 | 2 |
| #22582874 | 2 |
| #22582873 | 2 |
| #22582872 | 2 |
| #22582870 | 2 |
| #22582869 | 2 |
| #22582865 | 2 |
| #22582863 | 2 |
| #22582861 | 2 |
| #22582859 | 2 |
| #22582857 | 2 |
| #22582856 | 2 |
| #126×C281 | 2 |
| #563 | 281 |