Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
358 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 358 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. C2×#872 | C2 | semidirect |
| 3. C2×#825 | C2 | semidirect |
| 4. #5126 | C2 | semidirect |
| 5. C2×#805 | C2 | semidirect |
| 6. C3×#339 | C2 | semidirect |
| 7. #4532 | C2 | semidirect |
| 18. #897 | C4 | semidirect |
| 19. #895 | C4 | semidirect |
| 34. #339 | D3 | semidirect |
| 62. C3×C42 | D4 | semidirect |
| 69. C4×Dic3 | D4 | semidirect |
| 165. C42 | D12 | semidirect |
| 248. C3 | #1897 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #5524 | 2 |
| C2×#872 | 2 |
| C2×#825 | 2 |
| #5126 | 2 |
| C2×#805 | 2 |
| C3×#339 | 2 |
| #4532 | 2 |
| #1897 | 3 |