Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
252 conjugacy classes of subgroups; only the 67 normal subgroups are shown.
This group has 252 conjugacy classes of subgroups — too many to draw. Only its 67 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. #4835 | C2 | semidirect |
| 3. D3×C4⋊C8 | C2 | semidirect |
| 4. C3×#331 | C2 | semidirect |
| 5. #4544 | C2 | semidirect |
| 6. #4481 | C2 | semidirect |
| 7. #4481 | C2 | semidirect |
| 32. #331 | D3 | semidirect |
| 185. C3 | #1551 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #5716 | 2 |
| #4835 | 2 |
| D3×C4⋊C8 | 2 |
| C3×#331 | 2 |
| #4544 | 2 |
| #4481 | 2 |
| #1551 | 3 |