Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
598 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 598 conjugacy classes of subgroups — too many to draw. Only its 87 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×D3×C22⋊C4 | C2 | semidirect |
| 3. #4955 | C2 | semidirect |
| 4. C2×#806 | C2 | semidirect |
| 5. C2×#806 | C2 | semidirect |
| 6. C3×#342 | C2 | semidirect |
| 7. #4526 | C2 | semidirect |
| 11. C22×D12 | C4 | semidirect |
| 20. C2×(C2×D3)⋊C4 | C4 | semidirect |
| 34. #342 | D3 | semidirect |
| 42. C23×D3 | C2×C4 | semidirect |
| 48. C22×C3×C4 | C2×C4 | semidirect |
| 57. C22×Dic3 | C2×C4 | semidirect |
| 68. C3×C22⋊C4 | D4 | semidirect |
| 72. #217 | D4 | semidirect |
| 175. C22×C4 | C4×D3 | semidirect |
| 189. C22⋊C4 | D12 | semidirect |
| 221. C2×D3 | #99 | semidirect |
| 329. C3 | #1898 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#882 | 2 |
| C2×D3×C22⋊C4 | 2 |
| #4955 | 2 |
| C2×#806 | 2 |
| C3×#342 | 2 |
| #4526 | 2 |
| #1898 | 3 |