Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
396 conjugacy classes of subgroups; only the 217 normal subgroups are shown.
This group has 396 conjugacy classes of subgroups — too many to draw. Only its 217 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 |
|---|---|---|
| 4. #4830 | C2 | semidirect |
| 6. C8×Dic6 | C2 | semidirect |
| 36. C2×Dic6 | C8 | semidirect |
| 152. C3 | #2982 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×Dic6 | 2 |
| C3×#431 | 2 |
| #4925 | 2 |
| #4830 | 2 |
| #4718 | 2 |
| C8×Dic6 | 2 |
| #2982 | 3 |