Finite Group DatabasebetaFinite Group DatabasebetaOrder 2432.
950 conjugacy classes of subgroups; only the 449 normal subgroups are shown.
This group has 950 conjugacy classes of subgroups — too many to draw. Only its 449 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×D19 |
| commutator, socle, cosocle | C22×C19 | C25 |
| Fitting | C19×#564 | C2 |
| hypercenter | #564 | D19 |
| hypocenter | C19 | #3567 |
| LCS | G ▷ C22×C19 ▷ C19 | |
| UCS | C1 ◁ C22 ◁ #564 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #11927292 | C2 | semidirect |
| 2. #11927247 | C2 | semidirect |
| 3. #11927226 | C2 | semidirect |
| 4. #11927150 | C2 | semidirect |
| 5. #11927142 | C2 | semidirect |
| 6. #11927079 | C2 | semidirect |
| 7. C19×#564 | C2 | semidirect |
| 97. #564 | D19 | semidirect |
| 138. C19 | #3567 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11927292 | 2 |
| #11927247 | 2 |
| #11927226 | 2 |
| #11927150 | 2 |
| #11927142 | 2 |
| #11927079 | 2 |
| C19×#564 | 2 |
| #3567 | 19 |