Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
360 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 360 conjugacy classes of subgroups — too many to draw. Only its 115 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. #5568 | C2 | semidirect |
| 2. C3×C4×Q16 | C2 | semidirect |
| 4. #5183 | C2 | semidirect |
| 5. #5028 | C2 | semidirect |
| 6. #4873 | C2 | semidirect |
| 8. #4818 | C2 | semidirect |
| 9. #4798 | C2 | semidirect |
| 11. C8×Dic6 | C2 | semidirect |
| 49. C4×Q16 | D3 | semidirect |
| 224. C3 | #3393 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #5568 | 2 |
| C3×C4×Q16 | 2 |
| #5191 | 2 |
| #5183 | 2 |
| #5028 | 2 |
| #4873 | 2 |
| #4872 | 2 |
| #4818 | 2 |
| #4798 | 2 |
| #4696 | 2 |
| C8×Dic6 | 2 |
| #3393 | 3 |