Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
184 conjugacy classes of subgroups; only the 53 normal subgroups are shown.
This group has 184 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×SD32 | C2 | semidirect |
| 2. #5191 | C2 | semidirect |
| 3. C2×#829 | C2 | semidirect |
| 4. #5155 | C2 | semidirect |
| 6. C2×#800 | C2 | semidirect |
| 7. Dic3×C16 | C2 | semidirect |
| 26. C2×SD32 | D3 | semidirect |
| 146. C3 | #2249 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×SD32 | 2 |
| #5191 | 2 |
| C2×#829 | 2 |
| #5155 | 2 |
| C2×#826 | 2 |
| C2×#800 | 2 |
| Dic3×C16 | 2 |
| #2249 | 3 |