Finite Group DatabasebetaFinite Group DatabasebetaOrder 2432.
396 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 396 conjugacy classes of subgroups — too many to draw. Only its 125 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. #11927264 | C2 | semidirect |
| 2. #11926890 | C2 | semidirect |
| 3. #11926865 | C2 | semidirect |
| 4. #11926829 | C2 | semidirect |
| 5. #11926771 | C2 | semidirect |
| 6. #11926741 | C2 | semidirect |
| 7. #11926706 | C2 | semidirect |
| 8. C4×#64528 | C2 | semidirect |
| 9. D4×C19⋊C8 | C2 | semidirect |
| 10. #11926540 | C2 | semidirect |
| 168. C19 | #3304 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11927264 | 2 |
| #11926890 | 2 |
| #11926865 | 2 |
| #11926829 | 2 |
| #11926771 | 2 |
| #11926741 | 2 |
| #11926706 | 2 |
| C4×#64528 | 2 |
| D4×C19⋊C8 | 2 |
| #11926540 | 2 |
| C19×#550 | 2 |
| #3304 | 19 |