Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
200 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 200 conjugacy classes of subgroups — too many to draw. Only its 57 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. #4705 | C2 | semidirect |
| 3. #4705 | C2 | semidirect |
| 4. C3×#330 | C2 | semidirect |
| 5. #4543 | C2 | semidirect |
| 6. #4464 | C2 | semidirect |
| 7. #4464 | C2 | semidirect |
| 32. #330 | D3 | semidirect |
| 189. C3 | #1535 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #5691 | 2 |
| #4705 | 2 |
| C3×#330 | 2 |
| #4543 | 2 |
| #4464 | 2 |
| #1535 | 3 |