Finite Group DatabasebetaFinite Group DatabasebetaOrder 2432.
712 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 712 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 | C2×C19×#120 | C2 |
| hypercenter | C2×#120 | D19 |
| hypocenter | C19 | #2812 |
| LCS | G ▷ C23×C19 ▷ C19 | |
| UCS | C1 ◁ C23 ◁ C2×#120 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#10597399 | C2 | semidirect |
| 2. #11926472 | C2 | semidirect |
| 3. #11926459 | C2 | semidirect |
| 4. #11926458 | C2 | semidirect |
| 5. #11926452 | C2 | semidirect |
| 6. #11926400 | C2 | semidirect |
| 7. C2×C19×#120 | C2 | semidirect |
| 11. C22×C22⋊D19 | C22 | semidirect |
| 18. C2×C22⋊Dic19 | C22 | semidirect |
| 19. C2×(C2×D19)⋊C4 | C22 | semidirect |
| 20. C2×Dic19⋊C4 | C22 | semidirect |
| 21. C19⋊#95 | C22 | semidirect |
| 22. C19⋊#95 | C22 | semidirect |
| 25. C24×C19 | D4 | semidirect |
| 100. C2×#120 | D19 | semidirect |
| 127. C19 | #2812 | semidirect |
| 131. C24 | C22⋊D19 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#10597399 | 2 |
| #11926472 | 2 |
| #11926459 | 2 |
| #11926458 | 2 |
| #11926452 | 2 |
| #11926400 | 2 |
| C2×C19×#120 | 2 |
| #2812 | 19 |