Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
380 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 380 conjugacy classes of subgroups — too many to draw. Only its 121 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 |
|---|---|---|
| 1. #5557 | C2 | semidirect |
| 2. C3×C4×D8 | C2 | semidirect |
| 4. #5155 | C2 | semidirect |
| 5. C4×#214 | C2 | semidirect |
| 6. #4887 | C2 | semidirect |
| 7. #4878 | C2 | semidirect |
| 8. #4778 | C2 | semidirect |
| 9. #4768 | C2 | semidirect |
| 10. C4×Dic12 | C2 | semidirect |
| 11. C4×D3×C8 | C2 | semidirect |
| 49. C4×D8 | D3 | semidirect |
| 231. C3 | #3168 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #5557 | 2 |
| C3×C4×D8 | 2 |
| #5157 | 2 |
| #5155 | 2 |
| C4×#214 | 2 |
| #4887 | 2 |
| #4878 | 2 |
| #4778 | 2 |
| #4768 | 2 |
| C4×Dic12 | 2 |
| C4×D3×C8 | 2 |
| #3168 | 3 |