Finite Group DatabasebetaFinite Group DatabasebetaOrder 2432.
392 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 392 conjugacy classes of subgroups — too many to draw. Only its 125 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. Q8×Dic38 | C2 | semidirect |
| 3. #11926891 | C2 | semidirect |
| 4. #11926889 | C2 | semidirect |
| 5. #11926834 | C2 | semidirect |
| 6. #11926833 | C2 | semidirect |
| 7. #11926744 | C2 | semidirect |
| 8. #11926742 | C2 | semidirect |
| 9. C8×Dic38 | C2 | semidirect |
| 10. #11926629 | C2 | semidirect |
| 11. C4×SD16×C19 | C2 | semidirect |
| 77. Q8×C19 | #41 | semidirect |
| 99. Dic38 | SD16 | semidirect |
| 131. C4×SD16 | D19 | semidirect |
| 166. C19 | #3362 | semidirect |
| 206. Q8 | #64541 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q8×Dic38 | 2 |
| #11927215 | 2 |
| #11926891 | 2 |
| #11926889 | 2 |
| #11926834 | 2 |
| #11926833 | 2 |
| #11926744 | 2 |
| #11926742 | 2 |
| C8×Dic38 | 2 |
| #11926629 | 2 |
| C4×SD16×C19 | 2 |
| #3362 | 19 |