Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
150 conjugacy classes of subgroups; only the 59 normal subgroups are shown.
This group has 150 conjugacy classes of subgroups — too many to draw. Only its 59 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 |
|---|---|---|
| 16. #829 | C4 | semidirect |
| 96. Dic3 | Q32 | semidirect |
| 123. C3 | C4×Q32 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Dic3×Q16 | 2 |
| C2×#829 | 2 |
| #4873 | 2 |
| C3×#358 | 2 |
| #4503 | 2 |
| Dic3×C16 | 2 |
| #4489 | 2 |
| C4×Q32 | 3 |