Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
345 conjugacy classes of subgroups; only the 84 normal subgroups are shown.
This group has 345 conjugacy classes of subgroups — too many to draw. Only its 84 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. #568⋊C3 | C2 | direct (N × H) |
| 3. C2×#131⋊C3 | C2 | semidirect |
| 4. C2×#568 | C3 | semidirect |
| 11. #131⋊C3 | C22 | semidirect |
| 14. #568 | C2×C3 | semidirect |
| 16. C2×#131 | C2×C3 | semidirect |
| 41. #131 | C22×C3 | semidirect |
| 170. C2 | #568⋊C3 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#41⋊C3 | 2 |
| #568⋊C3 | 2 |
| C2×#131⋊C3 | 2 |
| C2×#568 | 3 |
| C2×C3×M16 | 4 |