Finite Group DatabasebetaFinite Group DatabasebetaOrder 2432.
472 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 472 conjugacy classes of subgroups — too many to draw. Only its 149 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. C22×#64528 | C2 | semidirect |
| 3. #11926923 | C2 | semidirect |
| 4. #11926783 | C2 | semidirect |
| 5. #11926754 | C2 | semidirect |
| 6. #11926751 | C2 | semidirect |
| 7. #11926700 | C2 | semidirect |
| 8. #11926699 | C2 | semidirect |
| 9. C4×#64528 | C2 | semidirect |
| 71. #64528 | D4 | direct (N × H) |
| 88. D4×C19 | Q16 | semidirect |
| 114. C22×C19 | C2×Q16 | semidirect |
| 121. C4×C19 | C2×Q16 | semidirect |
| 172. C19 | D4×Q16 | semidirect |
| 224. D4 | #64528 | direct (N × H) |
| 244. C22 | C2×#64528 | semidirect |
| 254. C4 | C2×#64528 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#64528 | 2 |
| D4×Dic38 | 2 |
| #11926923 | 2 |
| #11926783 | 2 |
| #11926754 | 2 |
| #11926751 | 2 |
| #11926700 | 2 |
| #11926699 | 2 |
| C4×#64528 | 2 |
| D4×C19⋊C8 | 2 |
| D4×Q8×C19 | 2 |
| D4×Q16 | 19 |