Finite Group DatabasebetaFinite Group DatabasebetaOrder 32128.
930 conjugacy classes of subgroups; only the 451 normal subgroups are shown.
This group has 930 conjugacy classes of subgroups — too many to draw. Only its 451 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 | C24×D251 |
| commutator, socle, cosocle | C22×C251 | C25 |
| Fitting | #564×C251 | C2 |
| hypercenter | #564 | D251 |
| hypocenter | C251 | #3531 |
| LCS | G ▷ C22×C251 ▷ C251 | |
| UCS | C1 ◁ C22 ◁ #564 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #30632441 | C2 | semidirect |
| 2. #30632435 | C2 | semidirect |
| 3. #30632243 | C2 | semidirect |
| 4. #30632222 | C2 | semidirect |
| 5. #564×C251 | C2 | semidirect |
| 53. C251 | #3531 | semidirect |
| 55. #564 | D251 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #30632441 | 2 |
| #30632435 | 2 |
| #30632243 | 2 |
| #30632222 | 2 |
| #564×C251 | 2 |
| #3531 | 251 |