Finite Group DatabasebetaFinite Group DatabasebetaOrder 27584.
236 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 236 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 | C4×D4×C431 | C2 |
| hypercenter | C4×D4 | D431 |
| hypocenter | C431 | #555 |
| LCS | G ▷ C22×C431 ▷ C431 | |
| UCS | C1 ◁ C22 ◁ C4×D4 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #28352189 | C2 | semidirect |
| 2. #28352175 | C2 | semidirect |
| 3. #28352163 | C2 | semidirect |
| 4. #28352160 | C2 | semidirect |
| 5. C4×D1724 | C2 | semidirect |
| 6. #28352148 | C2 | semidirect |
| 7. #28352147 | C2 | semidirect |
| 8. C4×D4×C431 | C2 | semidirect |
| 57. C431 | #555 | semidirect |
| 64. C4×D4 | D431 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #28352189 | 2 |
| #28352175 | 2 |
| #28352163 | 2 |
| #28352160 | 2 |
| C4×D1724 | 2 |
| #28352148 | 2 |
| #28352147 | 2 |
| C4×D4×C431 | 2 |
| #555 | 431 |