Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
388 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 388 conjugacy classes of subgroups — too many to draw. Only its 125 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×#498 | C2 | semidirect |
| 4. #5094 | C2 | semidirect |
| 5. #5084 | C2 | semidirect |
| 6. #4864 | C2 | semidirect |
| 7. #4863 | C2 | semidirect |
| 8. #4862 | C2 | semidirect |
| 9. D3×#106 | C2 | semidirect |
| 10. C4×#204 | C2 | semidirect |
| 11. C8×D12 | C2 | semidirect |
| 44. #498 | D3 | semidirect |
| 131. D12 | SD16 | semidirect |
| 140. C3×C8 | #41 | semidirect |
| 218. C8 | #239 | semidirect |
| 241. C3 | #3335 | 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×#498 | 2 |
| #5094 | 2 |
| #5084 | 2 |
| #4864 | 2 |
| #4863 | 2 |
| #4862 | 2 |
| D3×#106 | 2 |
| C4×#204 | 2 |
| C8×D12 | 2 |
| #3335 | 3 |