Finite Group DatabasebetaFinite Group DatabasebetaOrder 2432.
758 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 758 conjugacy classes of subgroups — too many to draw. Only its 149 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×#64545 | C2 | semidirect |
| 2. C2×#10597388 | C2 | semidirect |
| 3. C2×#10597354 | C2 | semidirect |
| 4. #11927056 | C2 | semidirect |
| 5. #11926709 | C2 | semidirect |
| 6. #11926692 | C2 | semidirect |
| 7. #11926548 | C2 | semidirect |
| 8. #11926507 | C2 | semidirect |
| 9. C19×#419 | C2 | semidirect |
| 22. C2×#64528 | C22 | semidirect |
| 24. C2×#64527 | C22 | semidirect |
| 27. C2×D152 | C22 | semidirect |
| 28. C2×#64516 | C22 | semidirect |
| 29. #10597343 | C22 | semidirect |
| 30. #10597341 | C22 | semidirect |
| 34. C19×#103 | C22 | semidirect |
| 35. (C2×D19)⋊C8 | C22 | semidirect |
| 36. #10597266 | C22 | semidirect |
| 41. C2×Q8×C19 | D4 | semidirect |
| 57. C2×D76 | D4 | semidirect |
| 146. #419 | D19 | semidirect |
| 179. #103 | C2×D19 | semidirect |
| 182. C19 | #3005 | semidirect |
| 193. C2×Q8 | D76 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#64545 | 2 |
| C2×#10597388 | 2 |
| C2×#10597354 | 2 |
| #11927056 | 2 |
| #11926709 | 2 |
| #11926692 | 2 |
| #11926548 | 2 |
| #11926507 | 2 |
| C19×#419 | 2 |
| #3005 | 19 |