Finite Group DatabasebetaFinite Group DatabasebetaOrder 27584.
234 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 234 conjugacy classes of subgroups — too many to draw. Only its 99 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×D431 |
| commutator, socle, cosocle | C22×C431 | C24 |
| Fitting | #125×C431 | C2 |
| prime radical | #28352164 | C2 |
| hypercenter | #125 | D431 |
| hypocenter | C431 | #529 |
| LCS | G ▷ C22×C431 ▷ C431 | |
| UCS | C1 ◁ C22 ◁ #125 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #28352184 | C2 | semidirect |
| 2. #28352177 | C2 | semidirect |
| 3. #28352174 | C2 | semidirect |
| 4. #28352169 | C2 | semidirect |
| 6. #28352154 | C2 | semidirect |
| 7. #28352151 | C2 | semidirect |
| 8. #28352151 | C2 | semidirect |
| 9. #28352147 | C2 | semidirect |
| 10. C42×D431 | C2 | semidirect |
| 11. #125×C431 | C2 | semidirect |
| 74. C431 | #529 | semidirect |
| 77. #125 | D431 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #28352184 | 2 |
| #28352177 | 2 |
| #28352174 | 2 |
| #28352169 | 2 |
| #28352164 | 2 |
| #28352154 | 2 |
| #28352151 | 2 |
| #28352147 | 2 |
| C42×D431 | 2 |
| #125×C431 | 2 |
| #529 | 431 |