Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
196 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 196 conjugacy classes of subgroups — too many to draw. Only its 57 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. #5183 | C2 | semidirect |
| 3. C2×#828 | C2 | semidirect |
| 5. C2×#827 | C2 | semidirect |
| 6. C2×#800 | C2 | semidirect |
| 7. Dic3×C16 | C2 | semidirect |
| 27. C2×SD32 | D3 | semidirect |
| 50. C3×C16 | D4 | semidirect |
| 51. C3⋊C16 | D4 | semidirect |
| 105. C16 | #67 | semidirect |
| 115. Dic3 | SD32 | semidirect |
| 148. C3 | #2248 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×SD32 | 2 |
| #5183 | 2 |
| C2×#828 | 2 |
| #5151 | 2 |
| C2×#827 | 2 |
| C2×#800 | 2 |
| Dic3×C16 | 2 |
| #2248 | 3 |