Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
390 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 390 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. #5728 | C2 | semidirect |
| 3. C3×#475 | C2 | semidirect |
| 4. #5087 | C2 | semidirect |
| 5. #5031 | C2 | semidirect |
| 6. #4868 | C2 | semidirect |
| 7. #4852 | C2 | semidirect |
| 8. #4841 | C2 | semidirect |
| 9. #4833 | C2 | semidirect |
| 11. #4790 | C2 | semidirect |
| 47. #475 | 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 |
|---|---|
| #5728 | 2 |
| C4×#239 | 2 |
| C3×#475 | 2 |
| #5087 | 2 |
| #5031 | 2 |
| #4868 | 2 |
| #4852 | 2 |
| #4841 | 2 |
| #4833 | 2 |
| #4808 | 2 |
| #4790 | 2 |
| #3107 | 3 |