Finite Group DatabasebetaFinite Group DatabasebetaOrder 2432.
460 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 460 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.
| subgroup | G/H | |
|---|---|---|
| center | C2 | D4×D76 |
| commutator, cosocle | C2×C4×C19 | C24 |
| Frattini | C2×C4 | C23×D19 |
| Fitting | C19×#443 | C2 |
| socle | C2×C19 | D42 |
| hypercenter | #443 | D19 |
| hypocenter | C19 | #3291 |
| LCS | G ▷ C2×C4×C19 ▷ C2×C19 ▷ C19 | |
| UCS | C1 ◁ C2 ◁ C2×C4 ◁ #443 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #11927356 | C2 | semidirect |
| 2. #11927351 | C2 | semidirect |
| 3. #11926917 | C2 | semidirect |
| 4. #11926808 | C2 | semidirect |
| 5. #11926807 | C2 | semidirect |
| 6. #11926728 | C2 | semidirect |
| 7. #11926713 | C2 | semidirect |
| 8. #11926662 | C2 | semidirect |
| 9. C19×#443 | C2 | semidirect |
| 11. #10597435 | C22 | semidirect |
| 13. C19×#131 | C22 | semidirect |
| 14. #10597397 | C22 | semidirect |
| 21. #10597355 | C22 | semidirect |
| 27. C2×#64516 | C22 | semidirect |
| 28. C2×#64516 | C22 | semidirect |
| 29. #10597347 | C22 | semidirect |
| 31. #10597315 | C22 | semidirect |
| 32. C19×#108 | C22 | semidirect |
| 33. C19×#104 | C22 | semidirect |
| 34. C4×C8×C19 | C22 | semidirect |
| 35. #10597281 | C22 | semidirect |
| 36. #10597280 | C22 | semidirect |
| 37. #10597276 | C22 | semidirect |
| 38. #10597262 | C22 | semidirect |
| 54. Q16×C19 | D4 | semidirect |
| 55. SD16×C19 | D4 | semidirect |
| 56. D8×C19 | D4 | semidirect |
| 70. Dic76 | D4 | semidirect |
| 72. D152 | D4 | semidirect |
| 79. #64516 | D4 | semidirect |
| 134. #443 | D19 | semidirect |
| 159. #131 | C2×D19 | semidirect |
| 163. #108 | C2×D19 | semidirect |
| 165. #104 | C2×D19 | semidirect |
| 168. C4×C8 | C2×D19 | semidirect |
| 169. C19 | #3291 | semidirect |
| 188. Q16 | D76 | semidirect |
| 198. SD16 | D76 | semidirect |
| 202. D8 | D76 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11927356 | 2 |
| #11927351 | 2 |
| #11926917 | 2 |
| #11926808 | 2 |
| #11926807 | 2 |
| #11926728 | 2 |
| #11926713 | 2 |
| #11926662 | 2 |
| C19×#443 | 2 |
| #3291 | 19 |