Finite Group DatabasebetaFinite Group DatabasebetaOrder 2432.
392 conjugacy classes of subgroups; only the 139 normal subgroups are shown.
This group has 392 conjugacy classes of subgroups — too many to draw. Only its 139 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. #11926835 | C2 | semidirect |
| 5. #11926745 | C2 | semidirect |
| 6. C4×#64516 | C2 | semidirect |
| 7. C8×Q8×C19 | C2 | semidirect |
| 44. Q8×C19 | SD16 | semidirect |
| 58. Dic38 | #41 | semidirect |
| 78. C8×Q8 | D19 | semidirect |
| 100. C19 | #3362 | semidirect |
| 124. Q8 | #64516 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q8×Dic38 | 2 |
| #11927216 | 2 |
| #11926891 | 2 |
| #11926835 | 2 |
| #11926745 | 2 |
| C4×#64516 | 2 |
| C8×Q8×C19 | 2 |
| #3362 | 19 |