Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
936 conjugacy classes of subgroups; only the 285 normal subgroups are shown.
This group has 936 conjugacy classes of subgroups — too many to draw. Only its 285 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. C2×#926 | C2 | semidirect |
| 4. #5213 | C2 | semidirect |
| 5. #4939 | C2 | semidirect |
| 6. C4×(C2×D3)⋊C4 | C2 | semidirect |
| 7. #4929 | C2 | semidirect |
| 14. C2×#235 | C4 | semidirect |
| 29. C22×C42 | D3 | semidirect |
| 52. C2×D12 | C2×C4 | semidirect |
| 55. C2×C4×D3 | C2×C4 | semidirect |
| 58. C2×Dic6 | C2×C4 | semidirect |
| 95. C2×C3×C4 | C22⋊C4 | semidirect |
| 102. C2×C3×C4 | #41 | semidirect |
| 181. C2×C4 | (C2×D3)⋊C4 | semidirect |
| 186. C2×C4 | #235 | 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 |
| C22×C3×C42 | 2 |
| C2×#926 | 2 |
| #5213 | 2 |
| #4939 | 2 |
| C4×(C2×D3)⋊C4 | 2 |
| #4929 | 2 |
| #2297 | 3 |