Finite Group DatabasebetaFinite Group DatabasebetaOrder 17984.
270 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 270 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.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C23×D281 |
| commutator, socle, cosocle | C22×C281 | C24 |
| Fitting | #123×C281 | C2 |
| prime radical | C2×#17985137 | C2 |
| hypercenter | #123 | D281 |
| hypocenter | C281 | #536 |
| LCS | G ▷ C22×C281 ▷ C281 | |
| UCS | C1 ◁ C22 ◁ #123 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C22×Dic562 | C2 | semidirect |
| 3. #22582878 | C2 | semidirect |
| 4. #22582865 | C2 | semidirect |
| 5. #22582863 | C2 | semidirect |
| 6. #22582862 | C2 | semidirect |
| 7. #22582860 | C2 | semidirect |
| 8. #22582857 | C2 | semidirect |
| 9. #22582856 | C2 | semidirect |
| 10. #22582835 | C2 | semidirect |
| 11. #123×C281 | C2 | semidirect |
| 79. C281 | #536 | semidirect |
| 88. #123 | D281 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17985137 | 2 |
| C22×Dic562 | 2 |
| #22582878 | 2 |
| #22582865 | 2 |
| #22582863 | 2 |
| #22582862 | 2 |
| #22582860 | 2 |
| #22582857 | 2 |
| #22582856 | 2 |
| #22582835 | 2 |
| #123×C281 | 2 |
| #536 | 281 |