Finite Group DatabasebetaFinite Group DatabasebetaOrder 2432.
454 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 454 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 | #3290 |
| 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. #11927358 | C2 | semidirect |
| 2. #11927356 | C2 | semidirect |
| 3. #11927346 | C2 | semidirect |
| 4. #11926928 | C2 | semidirect |
| 5. #11926820 | C2 | semidirect |
| 6. #11926815 | C2 | semidirect |
| 7. #11926807 | C2 | semidirect |
| 8. #11926723 | C2 | semidirect |
| 9. #11926718 | C2 | semidirect |
| 10. #11926662 | C2 | semidirect |
| 11. C19×#443 | C2 | semidirect |
| 12. #10597436 | C22 | semidirect |
| 15. C19×#131 | C22 | semidirect |
| 16. #10597397 | C22 | semidirect |
| 27. #10597354 | C22 | semidirect |
| 28. C2×Dic76 | C22 | semidirect |
| 33. C2×#64516 | C22 | semidirect |
| 35. #10597347 | C22 | semidirect |
| 36. #10597321 | C22 | semidirect |
| 37. C19×#108 | C22 | semidirect |
| 38. C19×#104 | C22 | semidirect |
| 39. C4×C8×C19 | C22 | semidirect |
| 40. #10597281 | C22 | semidirect |
| 41. #10597280 | C22 | semidirect |
| 42. #10597276 | C22 | semidirect |
| 44. #10597262 | C22 | semidirect |
| 154. #443 | D19 | semidirect |
| 184. #131 | C2×D19 | semidirect |
| 187. #108 | C2×D19 | semidirect |
| 190. #104 | C2×D19 | semidirect |
| 193. C4×C8 | C2×D19 | semidirect |
| 194. C19 | #3290 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11927358 | 2 |
| #11927356 | 2 |
| #11927346 | 2 |
| #11926928 | 2 |
| #11926820 | 2 |
| #11926815 | 2 |
| #11926807 | 2 |
| #11926723 | 2 |
| #11926718 | 2 |
| #11926662 | 2 |
| C19×#443 | 2 |
| #3290 | 19 |