Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
206 conjugacy classes of subgroups; only the 49 normal subgroups are shown.
This group has 206 conjugacy classes of subgroups — too many to draw. Only its 49 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. #5143 | C2 | semidirect |
| 3. #4909 | C2 | semidirect |
| 4. C2×Dic24 | C2 | semidirect |
| 5. C3×#350 | C2 | semidirect |
| 6. #4517 | C2 | semidirect |
| 7. #4510 | C2 | semidirect |
| 32. #350 | 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 |
|---|---|
| #5753 | 2 |
| #5143 | 2 |
| #4909 | 2 |
| C2×Dic24 | 2 |
| C3×#350 | 2 |
| #4517 | 2 |
| #4510 | 2 |
| #2195 | 3 |