Finite Group DatabasebetaFinite Group DatabasebetaOrder 2432.
380 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 380 conjugacy classes of subgroups — too many to draw. Only its 121 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. #11927073 | C2 | semidirect |
| 2. #11926946 | C2 | semidirect |
| 3. #11926898 | C2 | semidirect |
| 4. #11926782 | C2 | semidirect |
| 6. #11926770 | C2 | semidirect |
| 7. Q16×Dic19 | C2 | semidirect |
| 8. SD16×Dic19 | C2 | semidirect |
| 9. D8×Dic19 | C2 | semidirect |
| 10. C4×C8×D19 | C2 | semidirect |
| 11. C19×#495 | C2 | semidirect |
| 116. #495 | D19 | semidirect |
| 157. C19 | #3168 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11927073 | 2 |
| #11926946 | 2 |
| #11926898 | 2 |
| #11926782 | 2 |
| #11926777 | 2 |
| #11926770 | 2 |
| Q16×Dic19 | 2 |
| SD16×Dic19 | 2 |
| D8×Dic19 | 2 |
| C4×C8×D19 | 2 |
| C19×#495 | 2 |
| #3168 | 19 |