Finite Group DatabasebetaFinite Group DatabasebetaOrder 2432.
488 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 488 conjugacy classes of subgroups — too many to draw. Only its 121 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. #11927095 | C2 | semidirect |
| 2. C4×D4×D19 | C2 | semidirect |
| 3. #11926864 | C2 | semidirect |
| 4. #11926831 | C2 | semidirect |
| 5. #11926740 | C2 | semidirect |
| 6. #11926739 | C2 | semidirect |
| 7. #11926679 | C2 | semidirect |
| 8. #11926655 | C2 | semidirect |
| 9. #11926653 | C2 | semidirect |
| 10. #11926600 | C2 | semidirect |
| 11. C19×#476 | C2 | semidirect |
| 15. C19×C4⋊Q8 | C22 | semidirect |
| 26. #10597339 | C22 | semidirect |
| 30. #10597320 | C22 | semidirect |
| 33. C19×#106 | C22 | semidirect |
| 34. C19×C4⋊C8 | C22 | semidirect |
| 36. #10597278 | C22 | semidirect |
| 38. #10597272 | C22 | semidirect |
| 40. #10597266 | C22 | semidirect |
| 41. #10597265 | C22 | semidirect |
| 42. C4⋊(C19⋊C8) | C22 | semidirect |
| 93. D4×C19 | #41 | semidirect |
| 112. D76 | #41 | semidirect |
| 152. #476 | D19 | semidirect |
| 171. C4⋊Q8 | C2×D19 | semidirect |
| 188. #106 | C2×D19 | semidirect |
| 190. C4⋊C8 | C2×D19 | semidirect |
| 197. C19 | #3109 | semidirect |
| 256. D4 | #64545 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11927095 | 2 |
| C4×D4×D19 | 2 |
| #11926864 | 2 |
| #11926831 | 2 |
| #11926740 | 2 |
| #11926739 | 2 |
| #11926679 | 2 |
| #11926655 | 2 |
| #11926653 | 2 |
| #11926600 | 2 |
| C19×#476 | 2 |
| #3109 | 19 |