Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
388 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 388 conjugacy classes of subgroups — too many to draw. Only its 123 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 |
|---|---|---|
| 3. C3×#487 | C2 | semidirect |
| 4. #5091 | C2 | semidirect |
| 5. #5090 | C2 | semidirect |
| 6. #4813 | C2 | semidirect |
| 7. #4811 | C2 | semidirect |
| 8. #4809 | C2 | semidirect |
| 9. D3×#103 | C2 | semidirect |
| 10. C4×Dic12 | C2 | semidirect |
| 44. #487 | D3 | semidirect |
| 131. D12 | Q16 | semidirect |
| 240. C3 | #3299 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #5730 | 2 |
| #5727 | 2 |
| C3×#487 | 2 |
| #5091 | 2 |
| #5090 | 2 |
| #4813 | 2 |
| #4811 | 2 |
| #4809 | 2 |
| D3×#103 | 2 |
| C4×Dic12 | 2 |
| C8×D12 | 2 |
| #3299 | 3 |