Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
152 conjugacy classes of subgroups; only the 47 normal subgroups are shown.
This group has 152 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. #4878 | C2 | semidirect |
| 3. C3×#357 | C2 | semidirect |
| 4. #4562 | C2 | semidirect |
| 5. #4509 | C2 | semidirect |
| 6. #4502 | C2 | semidirect |
| 7. #4491 | C2 | semidirect |
| 25. #357 | D3 | semidirect |
| 137. C3 | #2244 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #5151 | 2 |
| #4878 | 2 |
| C3×#357 | 2 |
| #4562 | 2 |
| #4509 | 2 |
| #4502 | 2 |
| #4491 | 2 |
| #2244 | 3 |