Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
178 conjugacy classes of subgroups; only the 53 normal subgroups are shown.
This group has 178 conjugacy classes of subgroups — too many to draw. Only its 53 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. C2×C3×Q32 | C2 | semidirect |
| 3. #5183 | C2 | semidirect |
| 4. C2×#829 | C2 | semidirect |
| 7. #4502 | C2 | semidirect |
| 25. C2×Q32 | D3 | semidirect |
| 143. C3 | #2251 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×Q32 | 2 |
| #5191 | 2 |
| #5183 | 2 |
| C2×#829 | 2 |
| C2×#828 | 2 |
| C2×#800 | 2 |
| #4502 | 2 |
| #2251 | 3 |