Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
372 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 372 conjugacy classes of subgroups — too many to draw. Only its 133 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. C3×#544 | C2 | semidirect |
| 3. #5093 | C2 | semidirect |
| 4. #5089 | C2 | semidirect |
| 5. #5069 | C2 | semidirect |
| 6. #5068 | C2 | semidirect |
| 7. #5004 | C2 | semidirect |
| 9. #4997 | C2 | semidirect |
| 10. C2×#810 | C2 | semidirect |
| 42. #544 | D3 | semidirect |
| 249. C3 | #3137 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#544 | 2 |
| #5526 | 2 |
| #5093 | 2 |
| #5089 | 2 |
| #5069 | 2 |
| #5068 | 2 |
| #5004 | 2 |
| #5002 | 2 |
| #4997 | 2 |
| C2×#810 | 2 |
| #4966 | 2 |
| #3137 | 3 |