Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
246 conjugacy classes of subgroups; only the 65 normal subgroups are shown.
This group has 246 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 |
|---|---|---|
| 2. #4837 | C2 | semidirect |
| 3. #4835 | C2 | semidirect |
| 4. C3×#331 | C2 | semidirect |
| 5. #4544 | C2 | semidirect |
| 6. #4486 | C2 | semidirect |
| 7. #4482 | C2 | semidirect |
| 32. #331 | D3 | semidirect |
| 189. C3 | #1557 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #5716 | 2 |
| #4837 | 2 |
| #4835 | 2 |
| C3×#331 | 2 |
| #4544 | 2 |
| #4486 | 2 |
| #4482 | 2 |
| #1557 | 3 |