Finite Group DatabasebetaFinite Group DatabasebetaOrder 2432.
388 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 388 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. #11927120 | C2 | semidirect |
| 2. #11926931 | C2 | semidirect |
| 3. #11926916 | C2 | semidirect |
| 4. #11926914 | C2 | semidirect |
| 5. #11926901 | C2 | semidirect |
| 6. #11926759 | C2 | semidirect |
| 7. #11926749 | C2 | semidirect |
| 8. #11926687 | C2 | semidirect |
| 9. #11926682 | C2 | semidirect |
| 10. #11926605 | C2 | semidirect |
| 11. C19×#540 | C2 | semidirect |
| 116. #540 | D19 | semidirect |
| 159. C19 | #3221 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11927120 | 2 |
| #11926931 | 2 |
| #11926916 | 2 |
| #11926914 | 2 |
| #11926901 | 2 |
| #11926759 | 2 |
| #11926749 | 2 |
| #11926687 | 2 |
| #11926682 | 2 |
| #11926605 | 2 |
| C19×#540 | 2 |
| #3221 | 19 |