Finite Group DatabasebetaFinite Group DatabasebetaOrder 2432.
488 conjugacy classes of subgroups; only the 143 normal subgroups are shown.
This group has 488 conjugacy classes of subgroups — too many to draw. Only its 143 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 | C23×D19 | C23 |
| hypercenter | #400 | D19 |
| hypocenter | C19 | #2628 |
| 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×#10597334 | C2 | semidirect |
| 3. #11926483 | C2 | semidirect |
| 6. #11926465 | C2 | semidirect |
| 8. #11926441 | C2 | semidirect |
| 9. #11926408 | C2 | semidirect |
| 11. C19×#400 | C2 | semidirect |
| 50. C2×C4×D19 | Q8 | semidirect |
| 126. #400 | D19 | semidirect |
| 165. C19 | #2628 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#10597334 | 2 |
| C2×#10597338 | 2 |
| #11926483 | 2 |
| #11926481 | 2 |
| #11926479 | 2 |
| #11926465 | 2 |
| #11926457 | 2 |
| #11926441 | 2 |
| #11926408 | 2 |
| #11926403 | 2 |
| C19×#400 | 2 |
| #2628 | 19 |