Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
362 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 362 conjugacy classes of subgroups — too many to draw. Only its 125 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 |
|---|---|---|
| 2. #5570 | C2 | semidirect |
| 3. C3×#446 | C2 | semidirect |
| 4. #4849 | C2 | semidirect |
| 6. #4845 | C2 | semidirect |
| 7. #4841 | C2 | semidirect |
| 8. #4715 | C2 | semidirect |
| 9. #4710 | C2 | semidirect |
| 10. C4×Dic12 | C2 | semidirect |
| 50. #446 | D3 | semidirect |
| 238. C3 | #3400 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #5585 | 2 |
| #5570 | 2 |
| C3×#446 | 2 |
| #4849 | 2 |
| #4848 | 2 |
| #4845 | 2 |
| #4841 | 2 |
| #4715 | 2 |
| #4710 | 2 |
| C4×Dic12 | 2 |
| #4693 | 2 |
| #3400 | 3 |