Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
616 conjugacy classes of subgroups; only the 221 normal subgroups are shown.
This group has 616 conjugacy classes of subgroups — too many to draw. Only its 221 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×C4×D12 | C2 | semidirect |
| 3. C2×C3×C4×C8 | C2 | semidirect |
| 4. C2×#821 | C2 | semidirect |
| 5. C2×#818 | C2 | semidirect |
| 6. C4×D24 | C2 | direct (N × H) |
| 15. C2×D24 | C4 | direct (N × H) |
| 18. C4×D12 | C22 | semidirect |
| 19. C3×C4×C8 | C22 | semidirect |
| 20. #821 | C22 | semidirect |
| 21. #818 | C22 | semidirect |
| 27. C2×C4×C8 | D3 | semidirect |
| 35. C2×D12 | C2×C4 | semidirect |
| 40. C2×C3×C8 | C2×C4 | semidirect |
| 48. D24 | C2×C4 | direct (N × H) |
| 62. C4×C8 | C2×D3 | semidirect |
| 69. C2×C3×C4 | D8 | semidirect |
| 80. D12 | C22×C4 | semidirect |
| 83. C3×C8 | C22×C4 | semidirect |
| 97. C2×C8 | C4×D3 | semidirect |
| 115. C3×C4 | C2×D8 | semidirect |
| 131. C2×C4 | D24 | direct (N × H) |
| 139. C8 | C2×C4×D3 | semidirect |
| 140. C2×C3 | C4×D8 | semidirect |
| 156. C4 | C2×D24 | direct (N × H) |
| 159. C3 | C2×C4×D8 | semidirect |
| 161. C2 | C4×D24 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×D24 | 2 |
| C2×C4×D12 | 2 |
| C2×C3×C4×C8 | 2 |
| C2×#821 | 2 |
| C2×#818 | 2 |
| C4×D24 | 2 |
| C2×C4×D8 | 3 |