Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
352 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 352 conjugacy classes of subgroups — too many to draw. Only its 133 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. #5543 | C2 | semidirect |
| 4. #5008 | C2 | semidirect |
| 5. #4878 | C2 | semidirect |
| 6. #4766 | C2 | semidirect |
| 7. #4682 | C2 | semidirect |
| 8. C8×Dic6 | C2 | semidirect |
| 42. C3×D8 | Q8 | semidirect |
| 98. D8 | Dic6 | semidirect |
| 158. C3 | #3380 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #5543 | 2 |
| C3×C4×D8 | 2 |
| Dic3×D8 | 2 |
| #5008 | 2 |
| #4878 | 2 |
| #4766 | 2 |
| #4682 | 2 |
| C8×Dic6 | 2 |
| #3380 | 3 |