Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
404 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 404 conjugacy classes of subgroups — too many to draw. Only its 149 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 |
|---|---|---|
| 1. Q8×D12 | C2 | semidirect |
| 2. C3×C8×Q8 | C2 | semidirect |
| 3. #4846 | C2 | semidirect |
| 5. #4682 | C2 | semidirect |
| 21. C8×Q8 | D3 | semidirect |
| 35. D24 | Q8 | direct (N × H) |
| 48. C3×Q8 | D8 | semidirect |
| 54. D12 | C2×Q8 | semidirect |
| 58. C3×C8 | C2×Q8 | semidirect |
| 83. Q8 | D24 | direct (N × H) |
| 92. C8 | D3×Q8 | semidirect |
| 106. C3 | Q8×D8 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q8×D12 | 2 |
| C3×C8×Q8 | 2 |
| #4846 | 2 |
| C4×D24 | 2 |
| #4682 | 2 |
| Q8×D8 | 3 |