Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
392 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 392 conjugacy classes of subgroups — too many to draw. Only its 123 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. #5722 | C2 | semidirect |
| 3. C3×#476 | C2 | semidirect |
| 4. #5088 | C2 | semidirect |
| 5. C4×#214 | C2 | semidirect |
| 6. #4870 | C2 | semidirect |
| 7. #4852 | C2 | semidirect |
| 8. #4848 | C2 | semidirect |
| 9. #4830 | C2 | semidirect |
| 10. #4762 | C2 | semidirect |
| 11. #4760 | C2 | semidirect |
| 47. #476 | D3 | semidirect |
| 139. Dic6 | SD16 | semidirect |
| 140. Dic6 | #41 | semidirect |
| 245. C3 | #3362 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #5722 | 2 |
| #5553 | 2 |
| C3×#476 | 2 |
| #5088 | 2 |
| C4×#214 | 2 |
| #4870 | 2 |
| #4852 | 2 |
| #4848 | 2 |
| #4830 | 2 |
| #4762 | 2 |
| #4760 | 2 |
| #3362 | 3 |