Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
336 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 336 conjugacy classes of subgroups — too many to draw. Only its 101 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. C4×C4⋊Dic3 | C2 | semidirect |
| 4. C4×#208 | C2 | semidirect |
| 7. C3×C4⋊Q8 | C4 | semidirect |
| 8. C3×#127 | C4 | semidirect |
| 9. C3×#124 | C4 | semidirect |
| 49. #208 | D4 | semidirect |
| 53. C4⋊Q8 | Dic3 | semidirect |
| 54. #127 | Dic3 | semidirect |
| 55. #124 | Dic3 | semidirect |
| 128. C3×C4 | #104 | semidirect |
| 175. C4 | #837 | semidirect |
| 178. C3 | #1980 | 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 |
| C4×C4⋊Dic3 | 2 |
| C4×#208 | 2 |
| #1980 | 3 |