Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
404 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 404 conjugacy classes of subgroups — too many to draw. Only its 123 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. D3×C4⋊Q8 | C2 | semidirect |
| 3. C3×#476 | C2 | semidirect |
| 4. #5084 | C2 | semidirect |
| 5. #5008 | C2 | semidirect |
| 6. #4863 | C2 | semidirect |
| 7. #4855 | C2 | semidirect |
| 8. #4842 | C2 | semidirect |
| 9. #4833 | C2 | semidirect |
| 10. #4777 | C2 | semidirect |
| 11. #4760 | C2 | semidirect |
| 53. #476 | D3 | semidirect |
| 276. C3 | #3227 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D3×C4⋊Q8 | 2 |
| #5548 | 2 |
| C3×#476 | 2 |
| #5084 | 2 |
| #5008 | 2 |
| #4863 | 2 |
| #4855 | 2 |
| #4842 | 2 |
| #4833 | 2 |
| #4777 | 2 |
| #4760 | 2 |
| #3227 | 3 |