Finite Group DatabasebetaFinite Group DatabasebetaOrder 2432.
350 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 350 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. #11927267 | C2 | semidirect |
| 2. #11927254 | C2 | semidirect |
| 3. #11926899 | C2 | semidirect |
| 4. #11926895 | C2 | semidirect |
| 5. #11926852 | C2 | semidirect |
| 6. #11926835 | C2 | semidirect |
| 8. #11926750 | C2 | semidirect |
| 9. C4×#64516 | C2 | semidirect |
| 11. C8×Q8×C19 | C2 | semidirect |
| 124. C8×Q8 | D19 | semidirect |
| 161. C19 | #3360 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11927267 | 2 |
| #11927254 | 2 |
| #11926899 | 2 |
| #11926895 | 2 |
| #11926852 | 2 |
| #11926835 | 2 |
| #11926760 | 2 |
| #11926750 | 2 |
| C4×#64516 | 2 |
| C4×D152 | 2 |
| C8×Q8×C19 | 2 |
| #3360 | 19 |