Finite Group DatabasebetaFinite Group DatabasebetaOrder 2432.
564 conjugacy classes of subgroups; only the 165 normal subgroups are shown.
This group has 564 conjugacy classes of subgroups — too many to draw. Only its 165 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×#64516 | C2 | semidirect |
| 2. C22×C8×D19 | C2 | semidirect |
| 3. C2×#10597343 | C2 | semidirect |
| 5. #11926774 | C2 | direct (N × H) |
| 6. C2×#10597267 | C2 | semidirect |
| 7. C2×#10597266 | C2 | semidirect |
| 8. C2×C19×#106 | C2 | semidirect |
| 21. C2×#64516 | C22 | semidirect |
| 23. C2×C8×D19 | C22 | semidirect |
| 25. #10597343 | C22 | semidirect |
| 28. C19×#106 | C22 | semidirect |
| 29. #10597267 | C22 | semidirect |
| 30. #10597266 | C22 | semidirect |
| 52. C2×C8×C19 | D4 | semidirect |
| 72. C22×D19 | SD16 | semidirect |
| 96. C8×C19 | C2×D4 | semidirect |
| 110. C2×D19 | C2×SD16 | semidirect |
| 123. C2×#106 | D19 | semidirect |
| 126. C2×C19 | #465 | semidirect |
| 151. #106 | C2×D19 | semidirect |
| 154. C19 | C2×#465 | semidirect |
| 180. C2×C8 | D76 | semidirect |
| 221. C8 | C2×D76 | semidirect |
| 243. C2 | #11926774 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#64516 | 2 |
| C22×C8×D19 | 2 |
| C2×#10597343 | 2 |
| C2×#10597341 | 2 |
| #11926774 | 2 |
| C2×#10597267 | 2 |
| C2×#10597266 | 2 |
| C2×C19×#106 | 2 |
| C2×#465 | 19 |