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. #5698 | C2 | semidirect |
| 3. C3×#499 | C2 | semidirect |
| 4. #5069 | C2 | semidirect |
| 5. #5067 | C2 | semidirect |
| 6. #4889 | C2 | semidirect |
| 7. #4886 | C2 | semidirect |
| 8. #4864 | C2 | semidirect |
| 9. #4852 | C2 | semidirect |
| 10. #4693 | C2 | semidirect |
| 11. #4689 | C2 | semidirect |
| 42. #499 | D3 | semidirect |
| 212. C3 | #3174 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #5698 | 2 |
| #5697 | 2 |
| C3×#499 | 2 |
| #5069 | 2 |
| #5067 | 2 |
| #4889 | 2 |
| #4886 | 2 |
| #4864 | 2 |
| #4852 | 2 |
| #4693 | 2 |
| #4689 | 2 |
| #3174 | 3 |