Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
360 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 360 conjugacy classes of subgroups — too many to draw. Only its 113 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 |
|---|---|---|
| 3. C2×#835 | C2 | semidirect |
| 5. #4529 | C2 | semidirect |
| 10. C3×C22⋊Q8 | C4 | semidirect |
| 55. C22⋊Q8 | Dic3 | semidirect |
| 180. C3 | #1873 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×C22⋊Q8 | 2 |
| C2×#926 | 2 |
| C2×#835 | 2 |
| C2×#830 | 2 |
| #4529 | 2 |
| #1873 | 3 |