Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
390 conjugacy classes of subgroups; only the 129 normal subgroups are shown.
This group has 390 conjugacy classes of subgroups — too many to draw. Only its 129 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. #5470 | C2 | semidirect |
| 3. C3×#431 | C2 | semidirect |
| 4. #4851 | C2 | semidirect |
| 5. #4849 | C2 | semidirect |
| 6. #4846 | C2 | semidirect |
| 7. #4841 | C2 | semidirect |
| 9. #4723 | C2 | semidirect |
| 10. C4×Dic12 | C2 | semidirect |
| 11. C4×#204 | C2 | semidirect |
| 54. #431 | D3 | semidirect |
| 267. C3 | #3107 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#235 | 2 |
| #5470 | 2 |
| C3×#431 | 2 |
| #4851 | 2 |
| #4849 | 2 |
| #4846 | 2 |
| #4841 | 2 |
| #4733 | 2 |
| #4723 | 2 |
| C4×Dic12 | 2 |
| C4×#204 | 2 |
| #3107 | 3 |