Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
794 conjugacy classes of subgroups; only the 165 normal subgroups are shown.
This group has 794 conjugacy classes of subgroups — too many to draw. Only its 165 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 |
|---|---|---|
| 2. C2×#935 | C2 | semidirect |
| 3. #5243 | C2 | direct (N × H) |
| 4. C2×#834 | C2 | semidirect |
| 11. C23×Dic3 | C22 | semidirect |
| 13. C2×#217 | C22 | semidirect |
| 15. #935 | C22 | semidirect |
| 17. #834 | C22 | semidirect |
| 40. C22×Dic3 | C23 | semidirect |
| 43. #217 | C23 | semidirect |
| 143. C2×C3 | #458 | semidirect |
| 159. C3 | C2×#458 | semidirect |
| 163. C2 | #5243 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×H(5,𝔽2) | 2 |
| C2×#935 | 2 |
| #5243 | 2 |
| C2×#834 | 2 |
| C2×#458 | 3 |