Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
388 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 388 conjugacy classes of subgroups — too many to draw. Only its 115 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. #5730 | C2 | semidirect |
| 3. C3×#487 | C2 | semidirect |
| 4. #5090 | C2 | semidirect |
| 5. #5084 | C2 | semidirect |
| 6. #4816 | C2 | semidirect |
| 7. #4808 | C2 | semidirect |
| 8. #4805 | C2 | semidirect |
| 9. #4803 | C2 | semidirect |
| 10. C4×#204 | C2 | semidirect |
| 11. #4688 | C2 | semidirect |
| 44. #487 | D3 | semidirect |
| 247. C3 | #3331 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #5730 | 2 |
| #5726 | 2 |
| C3×#487 | 2 |
| #5090 | 2 |
| #5084 | 2 |
| #4816 | 2 |
| #4808 | 2 |
| #4805 | 2 |
| #4803 | 2 |
| C4×#204 | 2 |
| #4688 | 2 |
| #3331 | 3 |