Finite Group DatabasebetaFinite Group DatabasebetaOrder 2432.
564 conjugacy classes of subgroups; only the 157 normal subgroups are shown.
This group has 564 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.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C22×#64527 | C2 | semidirect |
| 3. C2×C4×D76 | C2 | semidirect |
| 4. #11926756 | C2 | direct (N × H) |
| 5. C2×C4⋊(C19⋊C8) | C2 | semidirect |
| 6. C2×#10597292 | C2 | semidirect |
| 7. C2×#10597289 | C2 | semidirect |
| 8. C2×C19×#124 | C2 | semidirect |
| 14. C19×#124 | C22 | semidirect |
| 19. C2×#64527 | C22 | semidirect |
| 27. C4×D76 | C22 | semidirect |
| 28. #10597292 | C22 | semidirect |
| 29. #10597289 | C22 | semidirect |
| 30. C4⋊(C19⋊C8) | C22 | semidirect |
| 120. C2×#124 | D19 | semidirect |
| 127. C2×C19 | #463 | semidirect |
| 143. #124 | C2×D19 | semidirect |
| 154. C19 | C2×#463 | semidirect |
| 243. C2 | #11926756 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#64527 | 2 |
| C22×#64525 | 2 |
| C2×C4×D76 | 2 |
| #11926756 | 2 |
| C2×C4⋊(C19⋊C8) | 2 |
| C2×#10597292 | 2 |
| C2×#10597289 | 2 |
| C2×C19×#124 | 2 |
| C2×#463 | 19 |