Finite Group DatabasebetaFinite Group DatabasebetaOrder 2432.
492 conjugacy classes of subgroups; only the 127 normal subgroups are shown.
This group has 492 conjugacy classes of subgroups — too many to draw. Only its 127 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. #11927092 | C2 | semidirect |
| 2. C4×D4×D19 | C2 | semidirect |
| 3. #11926856 | C2 | semidirect |
| 4. #11926825 | C2 | semidirect |
| 5. #11926824 | C2 | semidirect |
| 6. #11926736 | C2 | semidirect |
| 7. #11926676 | C2 | semidirect |
| 8. D8×Dic19 | C2 | semidirect |
| 9. #11926624 | C2 | semidirect |
| 10. #11926596 | C2 | semidirect |
| 11. C19×#459 | C2 | semidirect |
| 16. C19×#127 | C22 | semidirect |
| 23. D4×Dic19 | C22 | semidirect |
| 32. #10597315 | C22 | semidirect |
| 33. C19×C4⋊C8 | C22 | semidirect |
| 34. C19×#102 | C22 | semidirect |
| 36. #10597289 | C22 | semidirect |
| 39. #10597275 | C22 | semidirect |
| 40. C8×Dic19 | C22 | semidirect |
| 41. #10597264 | C22 | semidirect |
| 42. C4⋊(C19⋊C8) | C22 | semidirect |
| 96. D4×C19 | #41 | semidirect |
| 112. D76 | #41 | semidirect |
| 119. C4×D19 | D8 | semidirect |
| 154. #459 | D19 | semidirect |
| 172. #127 | C2×D19 | semidirect |
| 190. C4⋊C8 | C2×D19 | semidirect |
| 194. #102 | C2×D19 | semidirect |
| 197. C19 | #3100 | semidirect |
| 256. D4 | #64543 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11927092 | 2 |
| C4×D4×D19 | 2 |
| #11926856 | 2 |
| #11926825 | 2 |
| #11926824 | 2 |
| #11926736 | 2 |
| #11926676 | 2 |
| D8×Dic19 | 2 |
| #11926624 | 2 |
| #11926596 | 2 |
| C19×#459 | 2 |
| #3100 | 19 |