Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
198 conjugacy classes of subgroups; only the 65 normal subgroups are shown.
This group has 198 conjugacy classes of subgroups — too many to draw. Only its 65 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 |
|---|---|---|
| 4. C3×#333 | C2 | semidirect |
| 5. #4546 | C2 | semidirect |
| 6. #4486 | C2 | semidirect |
| 7. #4482 | C2 | semidirect |
| 30. #333 | D3 | semidirect |
| 166. C3 | #1554 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #5728 | 2 |
| #4835 | 2 |
| #4833 | 2 |
| C3×#333 | 2 |
| #4546 | 2 |
| #4486 | 2 |
| #4482 | 2 |
| #1554 | 3 |