Finite Group DatabasebetaFinite Group DatabasebetaOrder 2432.
1102 conjugacy classes of subgroups; only the 197 normal subgroups are shown.
This group has 1102 conjugacy classes of subgroups — too many to draw. Only its 197 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, socle, cosocle | C23×C19 | C24 |
| Fitting, prime radical | C2×C19×#120 | C2 |
| hypercenter | C2×#120 | D19 |
| hypocenter | C19 | #2849 |
| LCS | G ▷ C23×C19 ▷ C19 | |
| UCS | C1 ◁ C23 ◁ C2×#120 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C24×Dic19 | C2 | semidirect |
| 2. C2×#10597381 | C2 | semidirect |
| 3. #11926424 | C2 | semidirect |
| 4. #11926416 | C2 | semidirect |
| 5. #11926405 | C2 | semidirect |
| 6. #11926400 | C2 | semidirect |
| 20. C2×C22⋊Dic19 | C22 | semidirect |
| 22. C2×Dic19⋊C4 | C22 | semidirect |
| 23. C19⋊#95 | C22 | semidirect |
| 41. C22×Dic19 | D4 | semidirect |
| 88. C22×C19 | #123 | semidirect |
| 125. C19 | #2849 | semidirect |
| 188. C22 | #10597381 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C24×Dic19 | 2 |
| C2×#10597381 | 2 |
| #11926424 | 2 |
| #11926416 | 2 |
| #11926405 | 2 |
| #11926400 | 2 |
| C2×C19×#120 | 2 |
| #2849 | 19 |