Finite Group DatabasebetaFinite Group DatabasebetaOrder 2432.
512 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 512 conjugacy classes of subgroups — too many to draw. Only its 133 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×#394 | C2 |
| prime radical | C22×D4×C19 | C22 |
| hypercenter | #394 | D19 |
| hypocenter | C19 | #2633 |
| LCS | G ▷ C23×C19 ▷ C19 | |
| UCS | C1 ◁ C23 ◁ #394 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#10597335 | C2 | semidirect |
| 3. #11926480 | C2 | semidirect |
| 4. #11926476 | C2 | semidirect |
| 5. #11926474 | C2 | semidirect |
| 6. #11926472 | C2 | semidirect |
| 8. #11926419 | C2 | semidirect |
| 9. #11926416 | C2 | semidirect |
| 10. #11926411 | C2 | semidirect |
| 169. C19 | #2633 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#10597335 | 2 |
| C2×D4×Dic19 | 2 |
| #11926480 | 2 |
| #11926476 | 2 |
| #11926474 | 2 |
| #11926472 | 2 |
| #11926458 | 2 |
| #11926419 | 2 |
| #11926416 | 2 |
| #11926411 | 2 |
| C19×#394 | 2 |
| #2633 | 19 |