Finite Group DatabasebetaFinite Group DatabasebetaOrder 2432.
418 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 418 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 |
|---|---|---|
| 2. #11927025 | C2 | semidirect |
| 3. #11926871 | C2 | semidirect |
| 4. #11926870 | C2 | semidirect |
| 5. #11926864 | C2 | semidirect |
| 6. #11926859 | C2 | semidirect |
| 7. #11926580 | C2 | semidirect |
| 8. #11926550 | C2 | semidirect |
| 9. C2×#10597266 | C2 | semidirect |
| 10. #11926512 | C2 | semidirect |
| 11. C19×#428 | C2 | semidirect |
| 23. #10597338 | C22 | semidirect |
| 24. C4⋊C4×D19 | C22 | semidirect |
| 29. C19×#107 | C22 | semidirect |
| 30. C19×#106 | C22 | semidirect |
| 33. (C2×D19)⋊C8 | C22 | semidirect |
| 34. (C2×D19)⋊C8 | C22 | semidirect |
| 37. #10597265 | C22 | semidirect |
| 38. #10597265 | C22 | semidirect |
| 39. #10597264 | C22 | semidirect |
| 40. #10597264 | C22 | semidirect |
| 135. #428 | D19 | semidirect |
| 165. #107 | C2×D19 | semidirect |
| 168. #106 | C2×D19 | semidirect |
| 175. C19 | #3096 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11927113 | 2 |
| #11927025 | 2 |
| #11926871 | 2 |
| #11926870 | 2 |
| #11926864 | 2 |
| #11926859 | 2 |
| #11926580 | 2 |
| #11926550 | 2 |
| C2×#10597266 | 2 |
| #11926512 | 2 |
| C19×#428 | 2 |
| #3096 | 19 |