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. #11927251 | C2 | semidirect |
| 2. #11927215 | C2 | semidirect |
| 3. #11926907 | C2 | semidirect |
| 4. #11926891 | C2 | semidirect |
| 5. #11926847 | C2 | semidirect |
| 6. #11926834 | C2 | semidirect |
| 7. #11926739 | C2 | semidirect |
| 8. #11926737 | C2 | semidirect |
| 9. #11926674 | C2 | semidirect |
| 10. #11926653 | C2 | semidirect |
| 11. C4×D8×C19 | C2 | semidirect |
| 80. D4×C19 | #41 | semidirect |
| 134. C4×D8 | D19 | semidirect |
| 170. C19 | #3366 | semidirect |
| 218. D4 | #64541 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11927251 | 2 |
| #11927215 | 2 |
| #11926907 | 2 |
| #11926891 | 2 |
| #11926847 | 2 |
| #11926834 | 2 |
| #11926739 | 2 |
| #11926737 | 2 |
| #11926674 | 2 |
| #11926653 | 2 |
| C4×D8×C19 | 2 |
| #3366 | 19 |