Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
578 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 578 conjugacy classes of subgroups — too many to draw. Only its 83 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. #5486 | C2 | semidirect |
| 3. #4955 | C2 | semidirect |
| 4. #4955 | C2 | semidirect |
| 5. C2×#806 | C2 | semidirect |
| 6. C3×#342 | C2 | semidirect |
| 7. #4527 | C2 | semidirect |
| 22. #882 | C4 | semidirect |
| 33. #342 | D3 | semidirect |
| 42. C23×D3 | C2×C4 | semidirect |
| 46. C22×C3×C4 | D4 | semidirect |
| 55. C22×Dic3 | D4 | semidirect |
| 64. C3×C22⋊C4 | C2×C4 | semidirect |
| 121. C22×D3 | C22⋊C4 | semidirect |
| 138. C2×Dic3 | C22⋊C4 | semidirect |
| 165. C22×C4 | D12 | semidirect |
| 180. C22⋊C4 | C4×D3 | semidirect |
| 310. C3 | #1889 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#882 | 2 |
| #5486 | 2 |
| #4955 | 2 |
| C2×#806 | 2 |
| C3×#342 | 2 |
| #4527 | 2 |
| #1889 | 3 |