Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
856 conjugacy classes of subgroups; only the 269 normal subgroups are shown.
This group has 856 conjugacy classes of subgroups — too many to draw. Only its 269 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. C22×C3×C42 | C2 | semidirect |
| 3. C22×#208 | C2 | semidirect |
| 4. C2×#805 | C2 | direct (N × H) |
| 11. C2×#235 | C4 | semidirect |
| 13. C22×D12 | C4 | semidirect |
| 15. C22×Dic6 | C4 | semidirect |
| 17. C2×C3×C42 | C22 | semidirect |
| 19. C2×#208 | C22 | semidirect |
| 21. #805 | C22 | direct (N × H) |
| 24. C22×C42 | D3 | semidirect |
| 42. #235 | C2×C4 | semidirect |
| 45. C2×D12 | C2×C4 | semidirect |
| 49. C2×Dic6 | C2×C4 | semidirect |
| 51. C3×C42 | C23 | semidirect |
| 53. #208 | C23 | semidirect |
| 69. C2×C42 | C2×D3 | semidirect |
| 92. D12 | C22×C4 | semidirect |
| 96. Dic6 | C22×C4 | semidirect |
| 126. C42 | C22×D3 | semidirect |
| 129. C22×C3 | #104 | semidirect |
| 170. C2×C3 | C2×#104 | semidirect |
| 177. C22 | #805 | direct (N × H) |
| 187. C3 | C22×#104 | semidirect |
| 191. C2 | C2×#805 | 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 |
| C22×C3×C42 | 2 |
| C22×#208 | 2 |
| C2×#805 | 2 |
| C22×#104 | 3 |