Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
206 conjugacy classes of subgroups; only the 47 normal subgroups are shown.
This group has 206 conjugacy classes of subgroups — too many to draw. Only its 47 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. C2×#829 | C2 | semidirect |
| 3. #4909 | C2 | semidirect |
| 4. #4896 | C2 | semidirect |
| 5. C3×#362 | C2 | semidirect |
| 6. #4515 | C2 | semidirect |
| 7. #4497 | C2 | semidirect |
| 30. #362 | D3 | semidirect |
| 172. C3 | #2195 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #5766 | 2 |
| C2×#829 | 2 |
| #4909 | 2 |
| #4896 | 2 |
| C3×#362 | 2 |
| #4515 | 2 |
| #4497 | 2 |
| #2195 | 3 |