Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
936 conjugacy classes of subgroups; only the 277 normal subgroups are shown.
This group has 936 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×C3×#117 | C2 | semidirect |
| 3. C22×C4×Dic3 | C2 | semidirect |
| 4. #4988 | C2 | semidirect |
| 5. #4973 | C2 | semidirect |
| 6. #4958 | C2 | semidirect |
| 7. C4×(C2×D3)⋊C4 | C2 | semidirect |
| 14. C2×#235 | C4 | semidirect |
| 28. C2×#117 | D3 | semidirect |
| 52. C2×D12 | C2×C4 | semidirect |
| 55. C2×C4×D3 | C2×C4 | semidirect |
| 58. C2×Dic6 | C2×C4 | semidirect |
| 94. C2×C3×C4 | C22⋊C4 | semidirect |
| 108. C2×Dic3 | #41 | semidirect |
| 182. C2×C4 | (C2×D3)⋊C4 | semidirect |
| 212. C3 | #2297 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#235 | 2 |
| C2×C3×#117 | 2 |
| C22×C4×Dic3 | 2 |
| #4988 | 2 |
| #4973 | 2 |
| #4958 | 2 |
| C4×(C2×D3)⋊C4 | 2 |
| #2297 | 3 |