Finite Group DatabasebetaFinite Group DatabasebetaOrder 2432.
386 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 386 conjugacy classes of subgroups — too many to draw. Only its 113 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. C4⋊Q8×D19 | C2 | semidirect |
| 3. #11926938 | C2 | semidirect |
| 4. #11926936 | C2 | semidirect |
| 5. #11926914 | C2 | semidirect |
| 6. #11926753 | C2 | semidirect |
| 7. #11926748 | C2 | semidirect |
| 8. #11926701 | C2 | semidirect |
| 10. #11926599 | C2 | semidirect |
| 11. C19×#491 | C2 | semidirect |
| 136. #491 | D19 | semidirect |
| 178. C19 | #3218 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4⋊Q8×D19 | 2 |
| #11927079 | 2 |
| #11926938 | 2 |
| #11926936 | 2 |
| #11926914 | 2 |
| #11926753 | 2 |
| #11926748 | 2 |
| #11926701 | 2 |
| #11926684 | 2 |
| #11926599 | 2 |
| C19×#491 | 2 |
| #3218 | 19 |