Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
424 conjugacy classes of subgroups; only the 145 normal subgroups are shown.
This group has 424 conjugacy classes of subgroups — too many to draw. Only its 145 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 |
|---|---|---|
| 3. C3×#487 | C2 | semidirect |
| 4. #5093 | C2 | semidirect |
| 5. #5079 | C2 | semidirect |
| 7. #4792 | C2 | semidirect |
| 9. #4681 | C2 | semidirect |
| 42. #487 | D3 | direct (N × H) |
| 199. D3 | #487 | direct (N × H) |
| 214. C3 | C2×#487 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D3×C4⋊Q8 | 2 |
| C3×#487 | 2 |
| #5093 | 2 |
| #5079 | 2 |
| D3×#103 | 2 |
| #4792 | 2 |
| C4×D3×C8 | 2 |
| #4681 | 2 |
| C2×#487 | 3 |