Finite Group DatabasebetaFinite Group DatabasebetaOrder 2432.
924 conjugacy classes of subgroups; only the 201 normal subgroups are shown.
This group has 924 conjugacy classes of subgroups — too many to draw. Only its 201 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 | C2×C19×#121 | C2 |
| hypercenter | C2×#121 | D19 |
| hypocenter | C19 | #2856 |
| LCS | G ▷ C23×C19 ▷ C19 | |
| UCS | C1 ◁ C23 ◁ C2×#121 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#10597386 | C2 | semidirect |
| 2. C2×#10597376 | C2 | semidirect |
| 3. C2×#10597385 | C2 | semidirect |
| 4. C22×C4×Dic19 | C2 | semidirect |
| 5. #11926447 | C2 | semidirect |
| 6. #11926445 | C2 | semidirect |
| 7. #11926444 | C2 | semidirect |
| 8. #11926413 | C2 | semidirect |
| 9. C2×C19×#121 | C2 | semidirect |
| 42. C22×C4×C19 | D4 | semidirect |
| 53. C22×Dic19 | D4 | semidirect |
| 69. C4×Dic19 | D4 | semidirect |
| 119. C22×C19 | #127 | semidirect |
| 132. C4×C19 | #121 | semidirect |
| 135. Dic19 | #121 | semidirect |
| 139. C2×#121 | D19 | semidirect |
| 175. C19 | #2856 | semidirect |
| 200. C22×C4 | C22⋊D19 | semidirect |
| 267. C22 | #10597386 | semidirect |
| 278. C4 | #10597385 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#10597386 | 2 |
| C2×#10597376 | 2 |
| C2×#10597385 | 2 |
| C22×C4×Dic19 | 2 |
| #11926447 | 2 |
| #11926445 | 2 |
| #11926444 | 2 |
| #11926413 | 2 |
| C2×C19×#121 | 2 |
| #2856 | 19 |