Finite Group DatabasebetaFinite Group DatabasebetaOrder 2432.
1056 conjugacy classes of subgroups; only the 169 normal subgroups are shown.
This group has 1056 conjugacy classes of subgroups — too many to draw. Only its 169 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×#381 | C2 |
| hypercenter | #381 | D19 |
| hypocenter | C19 | #2404 |
| LCS | G ▷ C23×C19 ▷ C19 | |
| UCS | C1 ◁ C23 ◁ #381 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C22×#64541 | C2 | semidirect |
| 2. C2×#10597328 | C2 | semidirect |
| 3. C22×(C2×D19)⋊C4 | C2 | semidirect |
| 4. #11926457 | C2 | semidirect |
| 5. #11926454 | C2 | semidirect |
| 6. #11926422 | C2 | semidirect |
| 7. #11926421 | C2 | semidirect |
| 8. C19×#381 | C2 | semidirect |
| 16. C22×D76 | C22 | semidirect |
| 17. C22×C4×D19 | C22 | semidirect |
| 18. C22×Dic38 | C22 | semidirect |
| 24. C2×(C2×D19)⋊C4 | C22 | semidirect |
| 26. C19×#95 | C22 | semidirect |
| 27. C19×#95 | C22 | semidirect |
| 28. C19⋊#95 | C22 | semidirect |
| 37. C22×C4×C19 | D4 | semidirect |
| 43. C2×C22⋊D19 | D4 | semidirect |
| 82. C22×D19 | #41 | semidirect |
| 134. #381 | D19 | semidirect |
| 160. #95 | C2×D19 | semidirect |
| 161. #95 | C2×D19 | semidirect |
| 162. C19 | #2404 | semidirect |
| 189. C22×C4 | D76 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#64541 | 2 |
| C2×#10597328 | 2 |
| C22×(C2×D19)⋊C4 | 2 |
| #11926457 | 2 |
| #11926454 | 2 |
| #11926422 | 2 |
| #11926421 | 2 |
| C19×#381 | 2 |
| #2404 | 19 |