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×#64541 | C2 | semidirect |
| 2. C2×#10597355 | C2 | semidirect |
| 3. C2×#10597354 | C2 | semidirect |
| 4. #11927055 | C2 | semidirect |
| 5. #11926708 | C2 | semidirect |
| 6. #11926691 | C2 | semidirect |
| 7. #11926554 | C2 | semidirect |
| 8. #11926550 | C2 | semidirect |
| 9. C19×#407 | C2 | semidirect |
| 23. #10597376 | C22 | semidirect |
| 27. #10597370 | C22 | semidirect |
| 30. C2×Dic76 | C22 | semidirect |
| 31. C2×D152 | C22 | semidirect |
| 32. C2×#64516 | C22 | semidirect |
| 33. C2×#64516 | C22 | semidirect |
| 34. C19×C22⋊C8 | C22 | semidirect |
| 35. #10597278 | C22 | semidirect |
| 36. #10597273 | C22 | semidirect |
| 57. C2×D76 | D4 | semidirect |
| 65. C2×Dic38 | D4 | semidirect |
| 148. #407 | D19 | semidirect |
| 181. C22⋊C8 | C2×D19 | semidirect |
| 182. C19 | #3005 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#64541 | 2 |
| C2×#10597355 | 2 |
| C2×#10597354 | 2 |
| #11927055 | 2 |
| #11926708 | 2 |
| #11926691 | 2 |
| #11926554 | 2 |
| #11926550 | 2 |
| C19×#407 | 2 |
| #3005 | 19 |