Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
166 conjugacy classes of subgroups; only the 49 normal subgroups are shown.
This group has 166 conjugacy classes of subgroups — too many to draw. Only its 49 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 |
|---|---|---|
| 1. #5183 | C2 | semidirect |
| 5. C3×#358 | C2 | semidirect |
| 6. Dic3⋊C16 | C2 | semidirect |
| 7. #4492 | C2 | semidirect |
| 28. #358 | D3 | semidirect |
| 109. Dic3 | SD32 | semidirect |
| 142. C3 | #2208 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #5183 | 2 |
| C2×#828 | 2 |
| C2×#800 | 2 |
| #4872 | 2 |
| C3×#358 | 2 |
| Dic3⋊C16 | 2 |
| #4492 | 2 |
| #2208 | 3 |