Finite Group DatabasebetaFinite Group DatabasebetaOrder 2432.
354 conjugacy classes of subgroups; only the 41 normal subgroups are shown.
This group has 354 conjugacy classes of subgroups — too many to draw. Only its 41 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. #11927176 | C2 | semidirect |
| 2. #11926731 | C2 | semidirect |
| 3. #11926712 | C2 | semidirect |
| 4. #11926336 | C2 | semidirect |
| 5. #11926331 | C2 | semidirect |
| 6. #11926330 | C2 | semidirect |
| 7. C19×B(4,𝔽2) | C2 | semidirect |
| 8. C19×H(5,𝔽2) | C22 | semidirect |
| 22. C19×#99 | C22 | semidirect |
| 25. #10597291 | C22 | semidirect |
| 26. #10597290 | C22 | semidirect |
| 27. C24×C19 | D4 | semidirect |
| 29. C23×D19 | D4 | semidirect |
| 48. C2×D76 | D4 | semidirect |
| 53. C22⋊C4×C19 | D4 | semidirect |
| 55. C22⋊Dic19 | D4 | semidirect |
| 62. C4×Dic19 | D4 | semidirect |
| 138. B(4,𝔽2) | D19 | semidirect |
| 151. H(5,𝔽2) | C2×D19 | semidirect |
| 169. #99 | C2×D19 | semidirect |
| 170. C19 | #2196 | semidirect |
| 173. C24 | C22⋊D19 | semidirect |
| 206. C22⋊C4 | C22⋊D19 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11927176 | 2 |
| #11926731 | 2 |
| #11926712 | 2 |
| #11926336 | 2 |
| #11926331 | 2 |
| #11926330 | 2 |
| C19×B(4,𝔽2) | 2 |
| #2196 | 19 |