Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
760 conjugacy classes of subgroups; only the 165 normal subgroups are shown.
This group has 760 conjugacy classes of subgroups — too many to draw. Only its 165 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. C2×#924 | C2 | semidirect |
| 3. C22×Dic12 | C2 | semidirect |
| 4. C22×#204 | C2 | semidirect |
| 5. C2×C3×C22⋊C8 | C2 | semidirect |
| 6. C2×#821 | C2 | semidirect |
| 7. C2×#816 | C2 | semidirect |
| 8. #4733 | C2 | direct (N × H) |
| 25. #924 | C22 | semidirect |
| 28. C2×Dic12 | C22 | semidirect |
| 30. C2×#204 | C22 | semidirect |
| 31. C3×C22⋊C8 | C22 | semidirect |
| 32. #821 | C22 | semidirect |
| 33. #816 | C22 | semidirect |
| 41. C2×C22⋊C8 | D3 | semidirect |
| 105. C22⋊C8 | C2×D3 | semidirect |
| 240. C2×C3 | #452 | semidirect |
| 264. C3 | C2×#452 | semidirect |
| 267. C2 | #4733 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#235 | 2 |
| C2×#924 | 2 |
| C22×Dic12 | 2 |
| C22×#204 | 2 |
| C2×C3×C22⋊C8 | 2 |
| C2×#821 | 2 |
| C2×#816 | 2 |
| #4733 | 2 |
| C2×#452 | 3 |