Finite Group DatabasebetaFinite Group DatabasebetaOrder 2432.
584 conjugacy classes of subgroups; only the 147 normal subgroups are shown.
This group has 584 conjugacy classes of subgroups — too many to draw. Only its 147 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×#400 | C2 |
| prime radical | C22×D76 | C22 |
| hypercenter | #400 | D19 |
| hypocenter | C19 | #2564 |
| LCS | G ▷ C23×C19 ▷ C19 | |
| UCS | C1 ◁ C23 ◁ #400 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#10597343 | C2 | semidirect |
| 3. #11926479 | C2 | semidirect |
| 4. #11926464 | C2 | semidirect |
| 5. #11926457 | C2 | semidirect |
| 6. #11926431 | C2 | semidirect |
| 8. #11926418 | C2 | semidirect |
| 9. #11926403 | C2 | semidirect |
| 10. #95×D19 | C2 | semidirect |
| 11. C19×#400 | C2 | semidirect |
| 50. C2×D76 | Q8 | semidirect |
| 137. #400 | D19 | semidirect |
| 178. C19 | #2564 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#10597343 | 2 |
| C2×#10597339 | 2 |
| #11926479 | 2 |
| #11926464 | 2 |
| #11926457 | 2 |
| #11926431 | 2 |
| #11926422 | 2 |
| #11926418 | 2 |
| #11926403 | 2 |
| #95×D19 | 2 |
| C19×#400 | 2 |
| #2564 | 19 |