Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
362 conjugacy classes of subgroups; only the 75 normal subgroups are shown.
This group has 362 conjugacy classes of subgroups — too many to draw. Only its 75 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×#869 | C2 | semidirect |
| 4. C2×#824 | C2 | semidirect |
| 5. #5004 | C2 | semidirect |
| 7. C3×#339 | C2 | semidirect |
| 36. #339 | D3 | semidirect |
| 245. C3 | #2005 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#909 | 2 |
| #5526 | 2 |
| C2×#869 | 2 |
| C2×#824 | 2 |
| #5004 | 2 |
| C2×#805 | 2 |
| C3×#339 | 2 |
| #2005 | 3 |