Finite Group DatabasebetaFinite Group DatabasebetaOrder 2432.
450 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 450 conjugacy classes of subgroups — too many to draw. Only its 117 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. #11927080 | C2 | semidirect |
| 2. C2×#10597339 | C2 | semidirect |
| 3. #11926857 | C2 | semidirect |
| 4. #11926843 | C2 | semidirect |
| 5. #11926762 | C2 | semidirect |
| 6. #11926694 | C2 | semidirect |
| 8. #11926655 | C2 | semidirect |
| 9. #11926647 | C2 | semidirect |
| 10. #11926598 | C2 | semidirect |
| 11. C19×#483 | C2 | semidirect |
| 16. #10597393 | C22 | semidirect |
| 17. Q8×Dic19 | C22 | semidirect |
| 28. #10597339 | C22 | semidirect |
| 30. #10597336 | C22 | semidirect |
| 33. C19×#106 | C22 | semidirect |
| 34. C19×#103 | C22 | semidirect |
| 38. #10597272 | C22 | semidirect |
| 39. Dic19⋊C8 | C22 | semidirect |
| 41. #10597266 | C22 | semidirect |
| 42. #10597264 | C22 | semidirect |
| 137. #483 | D19 | semidirect |
| 174. #106 | C2×D19 | semidirect |
| 176. #103 | C2×D19 | semidirect |
| 183. C19 | #3114 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11927080 | 2 |
| C2×#10597339 | 2 |
| #11926857 | 2 |
| #11926843 | 2 |
| #11926762 | 2 |
| #11926694 | 2 |
| #11926680 | 2 |
| #11926655 | 2 |
| #11926647 | 2 |
| #11926598 | 2 |
| C19×#483 | 2 |
| #3114 | 19 |