Finite Group DatabasebetaFinite Group DatabasebetaOrder 36224.
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×D283 |
| commutator, socle, cosocle | C22×C283 | C25 |
| Fitting | #564×C283 | C2 |
| hypercenter | #564 | D283 |
| hypocenter | C283 | #3531 |
| LCS | G ▷ C22×C283 ▷ C283 | |
| UCS | C1 ◁ C22 ◁ #564 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #31827219 | C2 | semidirect |
| 2. #31827213 | C2 | semidirect |
| 3. #31827021 | C2 | semidirect |
| 4. #31827000 | C2 | semidirect |
| 5. #564×C283 | C2 | semidirect |
| 53. C283 | #3531 | semidirect |
| 55. #564 | D283 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31827219 | 2 |
| #31827213 | 2 |
| #31827021 | 2 |
| #31827000 | 2 |
| #564×C283 | 2 |
| #3531 | 283 |