Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
162 conjugacy classes of subgroups; only the 65 normal subgroups are shown.
This group has 162 conjugacy classes of subgroups — too many to draw. Only its 65 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×Dic12 | C2 | semidirect |
| 4. C3×C4×C16 | C2 | semidirect |
| 6. #4505 | C2 | semidirect |
| 7. #4503 | C2 | semidirect |
| 20. #800 | C4 | direct (N × H) |
| 27. C4×C16 | D3 | semidirect |
| 40. Dic12 | C2×C4 | semidirect |
| 44. C3×C16 | C2×C4 | semidirect |
| 88. C16 | C4×D3 | semidirect |
| 94. C3×C4 | SD32 | semidirect |
| 127. C4 | #800 | direct (N × H) |
| 130. C3 | C4×SD32 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#800 | 2 |
| C4×Dic12 | 2 |
| C4×D24 | 2 |
| C3×C4×C16 | 2 |
| #4509 | 2 |
| #4505 | 2 |
| #4503 | 2 |
| C4×SD32 | 3 |