Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
392 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 392 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. #5728 | C2 | semidirect |
| 3. C3×#489 | C2 | semidirect |
| 4. #5089 | C2 | semidirect |
| 5. #5055 | C2 | semidirect |
| 6. #4804 | C2 | semidirect |
| 7. #4797 | C2 | semidirect |
| 8. #4772 | C2 | semidirect |
| 9. #4764 | C2 | semidirect |
| 10. #4714 | C2 | semidirect |
| 11. D3×#97 | C2 | semidirect |
| 51. #489 | D3 | semidirect |
| 268. C3 | #3135 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #5728 | 2 |
| #5668 | 2 |
| C3×#489 | 2 |
| #5089 | 2 |
| #5055 | 2 |
| #4804 | 2 |
| #4797 | 2 |
| #4772 | 2 |
| #4764 | 2 |
| #4714 | 2 |
| D3×#97 | 2 |
| #3135 | 3 |