Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
924 conjugacy classes of subgroups; only the 277 normal subgroups are shown.
This group has 924 conjugacy classes of subgroups — too many to draw. Only its 277 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. C3×C43 | C2 | semidirect |
| 4. #4939 | C2 | semidirect |
| 5. #4935 | C2 | semidirect |
| 14. #874 | C4 | direct (N × H) |
| 20. C43 | D3 | semidirect |
| 28. C2×D12 | C2×C4 | semidirect |
| 31. C3×C42 | C2×C4 | semidirect |
| 32. C3×C42 | D4 | semidirect |
| 69. C42 | C4×D3 | semidirect |
| 70. C42 | D12 | semidirect |
| 78. C3×C4 | C4×D4 | semidirect |
| 79. C3×C4 | #127 | semidirect |
| 106. C4 | C4×D12 | semidirect |
| 107. C4 | #874 | direct (N × H) |
| 108. C3 | C4×#127 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#874 | 2 |
| C2×C4×D12 | 2 |
| C3×C43 | 2 |
| #4939 | 2 |
| #4935 | 2 |
| C4×#127 | 3 |