Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
382 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 382 conjugacy classes of subgroups — too many to draw. Only its 115 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. #5721 | C2 | semidirect |
| 3. C3×#486 | C2 | semidirect |
| 4. #5087 | C2 | semidirect |
| 5. #5075 | C2 | semidirect |
| 6. #4764 | C2 | semidirect |
| 7. #4763 | C2 | semidirect |
| 8. #4762 | C2 | semidirect |
| 9. #4757 | C2 | semidirect |
| 10. C4×#204 | C2 | semidirect |
| 11. #4679 | C2 | semidirect |
| 45. #486 | D3 | semidirect |
| 139. Dic6 | #41 | semidirect |
| 243. C3 | #3368 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #5721 | 2 |
| #5718 | 2 |
| C3×#486 | 2 |
| #5087 | 2 |
| #5075 | 2 |
| #4764 | 2 |
| #4763 | 2 |
| #4762 | 2 |
| #4757 | 2 |
| C4×#204 | 2 |
| #4679 | 2 |
| #3368 | 3 |