Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
392 conjugacy classes of subgroups; only the 145 normal subgroups are shown.
This group has 392 conjugacy classes of subgroups — too many to draw. Only its 145 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. C3×#341 | C2 | semidirect |
| 4. #4558 | C2 | semidirect |
| 5. #4552 | C2 | semidirect |
| 23. #341 | D3 | direct (N × H) |
| 143. D3 | #341 | direct (N × H) |
| 157. C3 | C2×#341 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D3×M16 | 2 |
| C22×D3×C8 | 2 |
| C3×#341 | 2 |
| #4558 | 2 |
| #4552 | 2 |
| C2×#341 | 3 |