Finite Group DatabasebetaFinite Group DatabasebetaOrder 2432.
362 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 362 conjugacy classes of subgroups — too many to draw. Only its 115 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. #11927166 | C2 | semidirect |
| 2. #11926948 | C2 | semidirect |
| 3. #11926929 | C2 | semidirect |
| 4. #11926905 | C2 | semidirect |
| 5. #11926793 | C2 | semidirect |
| 6. #11926782 | C2 | semidirect |
| 8. #11926642 | C2 | semidirect |
| 9. C4×D152 | C2 | semidirect |
| 10. #11926498 | C2 | semidirect |
| 11. C4×Q16×C19 | C2 | semidirect |
| 121. C4×Q16 | D19 | semidirect |
| 156. C19 | #3175 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11927166 | 2 |
| #11926948 | 2 |
| #11926929 | 2 |
| #11926905 | 2 |
| #11926793 | 2 |
| #11926782 | 2 |
| #11926781 | 2 |
| #11926642 | 2 |
| C4×D152 | 2 |
| #11926498 | 2 |
| C4×Q16×C19 | 2 |
| #3175 | 19 |