Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
390 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 390 conjugacy classes of subgroups — too many to draw. Only its 111 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×#497 | C2 | semidirect |
| 4. #5187 | C2 | semidirect |
| 5. #5182 | C2 | semidirect |
| 6. #5173 | C2 | semidirect |
| 7. #5163 | C2 | semidirect |
| 8. #5086 | C2 | semidirect |
| 9. #5055 | C2 | semidirect |
| 10. #4714 | C2 | semidirect |
| 11. #4705 | C2 | semidirect |
| 47. #497 | D3 | semidirect |
| 276. C3 | #3216 | 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×#497 | 2 |
| #5187 | 2 |
| #5182 | 2 |
| #5173 | 2 |
| #5163 | 2 |
| #5086 | 2 |
| #5055 | 2 |
| #4714 | 2 |
| #4705 | 2 |
| #3216 | 3 |