Finite Group DatabasebetaFinite Group DatabasebetaOrder 2432.
396 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 396 conjugacy classes of subgroups — too many to draw. Only its 117 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. #11927094 | C2 | semidirect |
| 2. #11926939 | C2 | semidirect |
| 3. #11926934 | C2 | semidirect |
| 4. #11926914 | C2 | semidirect |
| 5. #11926910 | C2 | semidirect |
| 6. #11926766 | C2 | semidirect |
| 7. #11926759 | C2 | semidirect |
| 8. #11926704 | C2 | semidirect |
| 9. #11926687 | C2 | semidirect |
| 10. #11926601 | C2 | semidirect |
| 11. C19×#529 | C2 | semidirect |
| 136. #529 | D19 | semidirect |
| 183. C19 | #3219 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11927094 | 2 |
| #11926939 | 2 |
| #11926934 | 2 |
| #11926914 | 2 |
| #11926910 | 2 |
| #11926766 | 2 |
| #11926759 | 2 |
| #11926704 | 2 |
| #11926687 | 2 |
| #11926601 | 2 |
| C19×#529 | 2 |
| #3219 | 19 |