Finite Group DatabasebetaFinite Group DatabasebetaOrder 2432.
752 conjugacy classes of subgroups; only the 177 normal subgroups are shown.
This group has 752 conjugacy classes of subgroups — too many to draw. Only its 177 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×#390 | C2 |
| prime radical | C2×#10597386 | C2 |
| hypercenter | #390 | D19 |
| hypocenter | C19 | #2858 |
| LCS | G ▷ C23×C19 ▷ C19 | |
| UCS | C1 ◁ C23 ◁ #390 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#10597334 | C2 | semidirect |
| 3. C2×#10597331 | C2 | semidirect |
| 4. #11926447 | C2 | semidirect |
| 5. #11926446 | C2 | semidirect |
| 6. #11926445 | C2 | semidirect |
| 7. #11926444 | C2 | semidirect |
| 8. C42×Dic19 | C2 | semidirect |
| 9. C19×#390 | C2 | semidirect |
| 62. C4×Dic19 | D4 | semidirect |
| 114. C4×C19 | #124 | semidirect |
| 117. Dic19 | #124 | semidirect |
| 126. #390 | D19 | semidirect |
| 155. C19 | #2858 | semidirect |
| 243. C4 | #10597331 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#10597334 | 2 |
| C2×#10597386 | 2 |
| C2×#10597331 | 2 |
| #11926447 | 2 |
| #11926446 | 2 |
| #11926445 | 2 |
| #11926444 | 2 |
| C42×Dic19 | 2 |
| C19×#390 | 2 |
| #2858 | 19 |