Finite Group DatabasebetaFinite Group DatabasebetaOrder 2432.
336 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 336 conjugacy classes of subgroups — too many to draw. Only its 123 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. #11927272 | C2 | semidirect |
| 3. #11926894 | C2 | semidirect |
| 4. #11926851 | C2 | semidirect |
| 7. #11926751 | C2 | semidirect |
| 8. Q8×C19⋊C8 | C2 | semidirect |
| 9. C4×#64528 | C2 | semidirect |
| 156. C19 | #3364 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11927272 | 2 |
| #11926898 | 2 |
| #11926894 | 2 |
| #11926851 | 2 |
| #11926824 | 2 |
| #11926763 | 2 |
| #11926751 | 2 |
| Q8×C19⋊C8 | 2 |
| C4×#64528 | 2 |
| C4×#64526 | 2 |
| C19×#556 | 2 |
| #3364 | 19 |