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. #11927267 | C2 | semidirect |
| 3. #11926891 | C2 | semidirect |
| 4. #11926871 | C2 | semidirect |
| 5. #11926829 | C2 | semidirect |
| 6. #11926776 | C2 | semidirect |
| 7. #11926744 | C2 | semidirect |
| 8. #11926705 | C2 | semidirect |
| 9. C8×D76 | C2 | semidirect |
| 10. #11926539 | C2 | semidirect |
| 11. C4×Q16×C19 | C2 | semidirect |
| 131. C4×Q16 | D19 | semidirect |
| 168. C19 | #3304 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11927267 | 2 |
| #11927216 | 2 |
| #11926891 | 2 |
| #11926871 | 2 |
| #11926829 | 2 |
| #11926776 | 2 |
| #11926744 | 2 |
| #11926705 | 2 |
| C8×D76 | 2 |
| #11926539 | 2 |
| C4×Q16×C19 | 2 |
| #3304 | 19 |