Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
386 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 386 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. #5728 | C2 | semidirect |
| 3. C3×#474 | C2 | semidirect |
| 4. #5087 | C2 | semidirect |
| 5. #5019 | C2 | semidirect |
| 6. #4886 | C2 | semidirect |
| 7. #4875 | C2 | semidirect |
| 8. #4841 | C2 | semidirect |
| 9. #4837 | C2 | semidirect |
| 10. #4780 | C2 | semidirect |
| 11. #4762 | C2 | semidirect |
| 48. #474 | D3 | semidirect |
| 278. C3 | #3254 | 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 |
| #5019 | 2 |
| #4886 | 2 |
| #4875 | 2 |
| #4841 | 2 |
| #4837 | 2 |
| #4780 | 2 |
| #4762 | 2 |
| #3254 | 3 |