Finite Group DatabasebetaFinite Group DatabasebetaOrder 2432.
620 conjugacy classes of subgroups; only the 181 normal subgroups are shown.
This group has 620 conjugacy classes of subgroups — too many to draw. Only its 181 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 | C19×#384 | C2 |
| prime radical | C22×D76 | C22 |
| hypercenter | #384 | D19 |
| hypocenter | C19 | #2538 |
| LCS | G ▷ C23×C19 ▷ C19 | |
| UCS | C1 ◁ C23 ◁ #384 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#10597343 | C2 | semidirect |
| 2. C2×C4×Dic38 | C2 | semidirect |
| 4. #11926466 | C2 | semidirect |
| 6. #11926443 | C2 | semidirect |
| 7. #11926401 | C2 | semidirect |
| 8. C19×#384 | C2 | semidirect |
| 38. C2×D76 | Q8 | semidirect |
| 44. C2×Dic38 | D4 | semidirect |
| 107. C4×C19 | C22⋊Q8 | semidirect |
| 117. #384 | D19 | semidirect |
| 146. C19 | #2538 | semidirect |
| 228. C4 | #10597343 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#10597343 | 2 |
| C2×C4×Dic38 | 2 |
| C2×C4×D76 | 2 |
| #11926466 | 2 |
| #11926445 | 2 |
| #11926443 | 2 |
| #11926401 | 2 |
| C19×#384 | 2 |
| #2538 | 19 |