Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
154 conjugacy classes of subgroups; only the 53 normal subgroups are shown.
This group has 154 conjugacy classes of subgroups — too many to draw. Only its 53 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. #4717 | C2 | semidirect |
| 3. #4711 | C2 | semidirect |
| 4. C3×#347 | C2 | semidirect |
| 5. #4518 | C2 | semidirect |
| 6. #4516 | C2 | semidirect |
| 7. #4513 | C2 | semidirect |
| 20. #800 | C4 | semidirect |
| 21. D48 | C4 | semidirect |
| 28. #347 | D3 | semidirect |
| 38. Dic12 | C2×C4 | semidirect |
| 41. D24 | C2×C4 | semidirect |
| 46. C3×C16 | C2×C4 | semidirect |
| 92. C16 | C4×D3 | semidirect |
| 132. C3 | AGL(1,ℤ/16) | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #4908 | 2 |
| #4717 | 2 |
| #4711 | 2 |
| C3×#347 | 2 |
| #4518 | 2 |
| #4516 | 2 |
| #4513 | 2 |
| AGL(1,ℤ/16) | 3 |