Finite Group DatabasebetaFinite Group DatabasebetaOrder 2432.
596 conjugacy classes of subgroups; only the 217 normal subgroups are shown.
This group has 596 conjugacy classes of subgroups — too many to draw. Only its 217 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C23×D19 |
| commutator | C22×C19 | C23×C4 |
| Fitting, prime radical | C2×C19×#121 | C2 |
| socle, cosocle | C23×C19 | C24 |
| hypercenter | C2×#121 | D19 |
| hypocenter | C19 | #2333 |
| LCS | G ▷ C22×C19 ▷ C19 | |
| UCS | C1 ◁ C23 ◁ C2×#121 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #11926447 | C2 | semidirect |
| 2. #11926437 | C2 | semidirect |
| 3. #11926430 | C2 | semidirect |
| 4. #11926424 | C2 | semidirect |
| 5. #11926424 | C2 | semidirect |
| 6. #11926407 | C2 | semidirect |
| 7. C22⋊C4×Dic19 | C2 | semidirect |
| 8. C4×C22⋊Dic19 | C2 | semidirect |
| 14. C19×#121 | C4 | semidirect |
| 39. C2×D4×C19 | C2×C4 | semidirect |
| 42. C22×C4×C19 | C2×C4 | semidirect |
| 53. C4⋊C4×C19 | C2×C4 | semidirect |
| 54. C22⋊C4×C19 | C2×C4 | semidirect |
| 148. #121 | Dic19 | semidirect |
| 166. C19 | #2333 | semidirect |
| 174. C2×D4 | C2×Dic19 | semidirect |
| 184. C22×C4 | C2×Dic19 | semidirect |
| 189. C4⋊C4 | C2×Dic19 | semidirect |
| 196. C22⋊C4 | C2×Dic19 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11926447 | 2 |
| #11926437 | 2 |
| #11926430 | 2 |
| #11926424 | 2 |
| #11926407 | 2 |
| C22⋊C4×Dic19 | 2 |
| C4×C22⋊Dic19 | 2 |
| C2×C19×#121 | 2 |
| #2333 | 19 |