Finite Group DatabasebetaFinite Group DatabasebetaOrder 2432.
1056 conjugacy classes of subgroups; only the 185 normal subgroups are shown.
This group has 1056 conjugacy classes of subgroups — too many to draw. Only its 185 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 | C22×#41×C19 | C2 |
| hypercenter | C22×#41 | D19 |
| hypocenter | C19 | #2404 |
| LCS | G ▷ C23×C19 ▷ C19 | |
| UCS | C1 ◁ C23 ◁ C22×#41 | |
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. #11926455 | C2 | semidirect |
| 4. #11926452 | C2 | semidirect |
| 5. #11926424 | C2 | semidirect |
| 6. #11926423 | C2 | semidirect |
| 7. #11926407 | C2 | semidirect |
| 8. C22×#41×C19 | C2 | semidirect |
| 12. C22×Q8×C19 | C22 | semidirect |
| 14. C22×D4×C19 | C22 | semidirect |
| 16. C23×C4×C19 | C22 | semidirect |
| 20. C2×C22⋊Dic19 | C22 | semidirect |
| 26. C19⋊#95 | C22 | semidirect |
| 27. C19⋊#95 | C22 | semidirect |
| 28. C19⋊#95 | C22 | semidirect |
| 43. C2×D4×C19 | D4 | semidirect |
| 48. C22×C4×C19 | D4 | semidirect |
| 82. C22×D19 | #41 | semidirect |
| 127. C22×#41 | D19 | semidirect |
| 145. C22×Q8 | C2×D19 | semidirect |
| 148. C22×D4 | C2×D19 | semidirect |
| 151. C23×C4 | C2×D19 | semidirect |
| 162. C19 | #2404 | semidirect |
| 180. C2×D4 | C22⋊D19 | semidirect |
| 189. 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 |
| #11926455 | 2 |
| #11926452 | 2 |
| #11926424 | 2 |
| #11926423 | 2 |
| #11926407 | 2 |
| C22×#41×C19 | 2 |
| #2404 | 19 |