Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
812 conjugacy classes of subgroups; only the 165 normal subgroups are shown.
This group has 812 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 |
|---|---|---|
| 1. C22×#237 | C2 | semidirect |
| 2. C22×#213 | C2 | semidirect |
| 3. C22×#204 | C2 | semidirect |
| 4. C2×#895 | C2 | semidirect |
| 5. C2×C3×#102 | C2 | semidirect |
| 6. C2×(C2×D3)⋊C8 | C2 | semidirect |
| 7. C2×#810 | C2 | semidirect |
| 8. #4781 | C2 | direct (N × H) |
| 16. C2×#237 | C22 | semidirect |
| 24. C2×#213 | C22 | semidirect |
| 28. C2×#204 | C22 | semidirect |
| 30. #895 | C22 | semidirect |
| 31. C3×#102 | C22 | semidirect |
| 32. (C2×D3)⋊C8 | C22 | semidirect |
| 33. #810 | C22 | semidirect |
| 40. C2×#102 | D3 | semidirect |
| 47. C2×C3×D4 | D4 | semidirect |
| 72. C2×Dic6 | D4 | semidirect |
| 105. #102 | C2×D3 | semidirect |
| 122. C3×D4 | C2×D4 | semidirect |
| 144. Dic6 | C2×D4 | semidirect |
| 167. C2×D4 | D12 | semidirect |
| 233. D4 | C2×D12 | semidirect |
| 251. C2×C3 | #449 | semidirect |
| 279. C3 | C2×#449 | semidirect |
| 283. C2 | #4781 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#237 | 2 |
| C22×#213 | 2 |
| C22×#204 | 2 |
| C2×#895 | 2 |
| C2×C3×#102 | 2 |
| C2×(C2×D3)⋊C8 | 2 |
| C2×#810 | 2 |
| #4781 | 2 |
| C2×#449 | 3 |