Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
366 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 366 conjugacy classes of subgroups — too many to draw. Only its 113 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×#474 | C2 | semidirect |
| 4. #5087 | C2 | semidirect |
| 5. #5008 | C2 | semidirect |
| 6. #4885 | C2 | semidirect |
| 7. #4876 | C2 | semidirect |
| 8. #4842 | C2 | semidirect |
| 9. #4835 | C2 | semidirect |
| 10. #4779 | C2 | semidirect |
| 11. #4764 | C2 | semidirect |
| 53. #474 | D3 | semidirect |
| 270. C3 | #3235 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #5728 | 2 |
| #5548 | 2 |
| C3×#474 | 2 |
| #5087 | 2 |
| #5008 | 2 |
| #4885 | 2 |
| #4876 | 2 |
| #4842 | 2 |
| #4835 | 2 |
| #4779 | 2 |
| #4764 | 2 |
| #3235 | 3 |