Finite Group DatabasebetaFinite Group DatabasebetaOrder 2432.
472 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 472 conjugacy classes of subgroups — too many to draw. Only its 125 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. #11927055 | C2 | semidirect |
| 2. C2×#10597376 | C2 | semidirect |
| 3. #11926880 | C2 | semidirect |
| 4. #11926869 | C2 | semidirect |
| 5. #11926863 | C2 | semidirect |
| 6. #11926780 | C2 | semidirect |
| 7. #11926773 | C2 | semidirect |
| 8. #11926697 | C2 | semidirect |
| 9. #11926691 | C2 | semidirect |
| 10. #11926680 | C2 | semidirect |
| 11. C2×C19×C22⋊C8 | C2 | semidirect |
| 14. C2×#64541 | C22 | semidirect |
| 16. C22×C8×C19 | C22 | semidirect |
| 23. #10597376 | C22 | semidirect |
| 28. #10597372 | C22 | semidirect |
| 31. #10597370 | C22 | semidirect |
| 32. C2×D152 | C22 | semidirect |
| 33. C2×#64516 | C22 | semidirect |
| 36. C19×C22⋊C8 | C22 | semidirect |
| 37. #10597278 | C22 | semidirect |
| 38. #10597278 | C22 | semidirect |
| 39. #10597278 | C22 | semidirect |
| 40. #10597275 | C22 | semidirect |
| 41. #10597274 | C22 | semidirect |
| 42. #10597273 | C22 | semidirect |
| 161. C2×C22⋊C8 | D19 | semidirect |
| 176. C22×C8 | C2×D19 | semidirect |
| 200. C22⋊C8 | C2×D19 | semidirect |
| 201. C19 | #3188 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11927055 | 2 |
| C2×#10597376 | 2 |
| #11926880 | 2 |
| #11926869 | 2 |
| #11926863 | 2 |
| #11926780 | 2 |
| #11926773 | 2 |
| #11926697 | 2 |
| #11926691 | 2 |
| #11926680 | 2 |
| C2×C19×C22⋊C8 | 2 |
| #3188 | 19 |