Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
332 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 332 conjugacy classes of subgroups — too many to draw. Only its 79 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. C4×#235 | C2 | semidirect |
| 3. #5006 | C2 | semidirect |
| 4. #5005 | C2 | semidirect |
| 5. C2×#805 | C2 | semidirect |
| 6. C3×#339 | C2 | semidirect |
| 7. #4559 | C2 | semidirect |
| 18. #909 | C4 | semidirect |
| 20. #908 | C4 | semidirect |
| 36. #339 | D3 | semidirect |
| 49. C2×D12 | C2×C4 | semidirect |
| 54. C2×Dic6 | C2×C4 | semidirect |
| 57. C3×M16 | C2×C4 | semidirect |
| 160. M16 | C4×D3 | semidirect |
| 252. C3 | #1906 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #5748 | 2 |
| C4×#235 | 2 |
| #5006 | 2 |
| #5005 | 2 |
| C2×#805 | 2 |
| C3×#339 | 2 |
| #4559 | 2 |
| #1906 | 3 |