Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
360 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 360 conjugacy classes of subgroups — too many to draw. Only its 105 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×#837 | C2 | semidirect |
| 3. C42×Dic3 | C2 | semidirect |
| 4. #4924 | C2 | semidirect |
| 7. C3×C4⋊Q8 | C4 | semidirect |
| 8. C3×#127 | C4 | semidirect |
| 9. C3×#124 | C4 | semidirect |
| 39. C4×Dic3 | D4 | semidirect |
| 44. C4⋊Q8 | Dic3 | semidirect |
| 45. #127 | Dic3 | semidirect |
| 46. #124 | Dic3 | semidirect |
| 100. C3×C4 | #104 | semidirect |
| 136. C4 | #837 | semidirect |
| 140. C3 | #1962 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#532 | 2 |
| C2×#837 | 2 |
| C42×Dic3 | 2 |
| #4924 | 2 |
| #1962 | 3 |