Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
404 conjugacy classes of subgroups; only the 137 normal subgroups are shown.
This group has 404 conjugacy classes of subgroups — too many to draw. Only its 137 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 |
|---|---|---|
| 4. C3×#339 | C2 | semidirect |
| 5. #4555 | C2 | semidirect |
| 6. #4532 | C2 | semidirect |
| 7. #4523 | C2 | semidirect |
| 19. D3×M16 | C4 | semidirect |
| 22. #892 | C4 | semidirect |
| 23. D3×C4⋊C4 | C4 | semidirect |
| 28. #872 | C4 | semidirect |
| 36. #339 | D3 | semidirect |
| 52. C3×M16 | C2×C4 | semidirect |
| 58. C3×C42 | C2×C4 | semidirect |
| 68. C4×Dic3 | C2×C4 | semidirect |
| 70. #208 | C2×C4 | semidirect |
| 146. M16 | C4×D3 | semidirect |
| 164. C42 | C4×D3 | semidirect |
| 244. C3 | #1733 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D3×M16 | 2 |
| D3×#117 | 2 |
| C2×#872 | 2 |
| C3×#339 | 2 |
| #4555 | 2 |
| #4532 | 2 |
| #4523 | 2 |
| #1733 | 3 |