Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
320 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 320 conjugacy classes of subgroups — too many to draw. Only its 113 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 |
|---|---|---|
| 2. C3×#376 | C2 | semidirect |
| 4. C4×#208 | C2 | semidirect |
| 5. #4523 | C2 | semidirect |
| 13. C4×D12 | C4 | semidirect |
| 16. C4×Dic6 | C4 | semidirect |
| 18. #805 | C4 | semidirect |
| 24. #376 | D3 | semidirect |
| 38. C3×C42 | C2×C4 | semidirect |
| 48. #208 | C2×C4 | semidirect |
| 106. C42 | C4×D3 | semidirect |
| 160. C3 | #1759 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#235 | 2 |
| C3×#376 | 2 |
| C2×#805 | 2 |
| C4×#208 | 2 |
| #4523 | 2 |
| #1759 | 3 |