Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
418 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 418 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. #5553 | C2 | semidirect |
| 3. C3×C4×SD16 | C2 | semidirect |
| 4. #5176 | C2 | semidirect |
| 5. #5027 | C2 | semidirect |
| 6. #5015 | C2 | semidirect |
| 7. #4869 | C2 | semidirect |
| 8. #4819 | C2 | semidirect |
| 9. #4786 | C2 | semidirect |
| 10. #4695 | C2 | semidirect |
| 11. #4679 | C2 | semidirect |
| 52. C4×SD16 | D3 | semidirect |
| 148. C3×C8 | #41 | semidirect |
| 236. C8 | #235 | semidirect |
| 262. C3 | #3399 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #5585 | 2 |
| #5553 | 2 |
| C3×C4×SD16 | 2 |
| #5176 | 2 |
| #5027 | 2 |
| #5015 | 2 |
| #4869 | 2 |
| #4819 | 2 |
| #4786 | 2 |
| #4695 | 2 |
| #4679 | 2 |
| #3399 | 3 |