Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
186 conjugacy classes of subgroups; only the 49 normal subgroups are shown.
This group has 186 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 |
|---|---|---|
| 1. #5151 | C2 | semidirect |
| 2. C2×#826 | C2 | semidirect |
| 3. C2×D48 | C2 | semidirect |
| 4. #4872 | C2 | semidirect |
| 5. C3×#357 | C2 | semidirect |
| 6. Dic3⋊C16 | C2 | semidirect |
| 7. #4491 | C2 | semidirect |
| 28. #357 | D3 | semidirect |
| 46. D24 | D4 | semidirect |
| 115. Dic3 | D16 | semidirect |
| 156. C3 | #2206 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #5151 | 2 |
| C2×#826 | 2 |
| C2×D48 | 2 |
| #4872 | 2 |
| C3×#357 | 2 |
| Dic3⋊C16 | 2 |
| #4491 | 2 |
| #2206 | 3 |