Finite Group DatabasebetaFinite Group DatabasebetaOrder 2432.
824 conjugacy classes of subgroups; only the 157 normal subgroups are shown.
This group has 824 conjugacy classes of subgroups — too many to draw. Only its 157 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 | #2617 |
| 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×#10597383 | C2 | semidirect |
| 2. C22×(C2×D19)⋊C4 | C2 | semidirect |
| 3. #11926470 | C2 | semidirect |
| 4. #11926460 | C2 | semidirect |
| 5. #11926452 | C2 | semidirect |
| 6. #11926424 | C2 | semidirect |
| 7. #11926404 | C2 | semidirect |
| 8. C2×C19×#121 | C2 | semidirect |
| 11. C22×D4×C19 | C22 | semidirect |
| 16. C2×C4⋊C4×C19 | C22 | semidirect |
| 17. C2×C22⋊C4×C19 | C22 | semidirect |
| 19. C2×C22⋊Dic19 | C22 | semidirect |
| 25. C2×C4⋊Dic19 | C22 | semidirect |
| 26. C19⋊#95 | C22 | semidirect |
| 27. C19⋊#95 | C22 | semidirect |
| 34. C23×D19 | D4 | semidirect |
| 42. C22×C4×C19 | D4 | semidirect |
| 126. C2×#121 | D19 | semidirect |
| 145. C22×D4 | C2×D19 | semidirect |
| 151. C2×C4⋊C4 | C2×D19 | semidirect |
| 158. C2×C22⋊C4 | C2×D19 | semidirect |
| 161. C19 | #2617 | semidirect |
| 183. C22×C4 | C22⋊D19 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#10597383 | 2 |
| C22×(C2×D19)⋊C4 | 2 |
| #11926470 | 2 |
| #11926460 | 2 |
| #11926452 | 2 |
| #11926424 | 2 |
| #11926404 | 2 |
| C2×C19×#121 | 2 |
| #2617 | 19 |