Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
362 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 362 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. #5543 | C2 | semidirect |
| 3. C3×C4×SD16 | C2 | semidirect |
| 4. #5165 | C2 | semidirect |
| 5. #5021 | C2 | semidirect |
| 7. #4871 | C2 | semidirect |
| 8. #4800 | C2 | semidirect |
| 9. #4756 | C2 | semidirect |
| 10. #4694 | C2 | semidirect |
| 11. C8×Dic6 | C2 | semidirect |
| 51. C4×SD16 | D3 | semidirect |
| 239. C3 | #3361 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #5585 | 2 |
| #5543 | 2 |
| C3×C4×SD16 | 2 |
| #5165 | 2 |
| #5021 | 2 |
| #5015 | 2 |
| #4871 | 2 |
| #4800 | 2 |
| #4756 | 2 |
| #4694 | 2 |
| C8×Dic6 | 2 |
| #3361 | 3 |