Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
428 conjugacy classes of subgroups; only the 127 normal subgroups are shown.
This group has 428 conjugacy classes of subgroups — too many to draw. Only its 127 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. C4×D3×Q8 | C2 | semidirect |
| 3. C3×#475 | C2 | semidirect |
| 4. #5094 | C2 | semidirect |
| 5. #5027 | C2 | semidirect |
| 6. #4863 | C2 | semidirect |
| 7. #4852 | C2 | semidirect |
| 8. #4848 | C2 | semidirect |
| 9. #4833 | C2 | semidirect |
| 10. #4806 | C2 | semidirect |
| 11. #4788 | C2 | semidirect |
| 48. #475 | D3 | semidirect |
| 130. C3×Q8 | #41 | semidirect |
| 153. C4×D3 | SD16 | semidirect |
| 156. Dic6 | #41 | semidirect |
| 225. Q8 | #239 | semidirect |
| 275. C3 | #3103 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #5725 | 2 |
| C4×D3×Q8 | 2 |
| C3×#475 | 2 |
| #5094 | 2 |
| #5027 | 2 |
| #4863 | 2 |
| #4852 | 2 |
| #4848 | 2 |
| #4833 | 2 |
| #4806 | 2 |
| #4788 | 2 |
| #3103 | 3 |