Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
384 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 384 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. #5585 | C2 | semidirect |
| 2. C3×C4×Q16 | C2 | semidirect |
| 3. #5191 | C2 | semidirect |
| 4. #5027 | C2 | semidirect |
| 5. #4872 | C2 | semidirect |
| 6. #4819 | C2 | semidirect |
| 8. C8×Dic6 | C2 | semidirect |
| 35. C4×Q16 | D3 | semidirect |
| 168. C3 | #3396 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #5585 | 2 |
| C3×C4×Q16 | 2 |
| #5191 | 2 |
| #5027 | 2 |
| #4872 | 2 |
| #4819 | 2 |
| #4695 | 2 |
| C8×Dic6 | 2 |
| #3396 | 3 |