Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
618 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 618 conjugacy classes of subgroups — too many to draw. Only its 105 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. C3×#407 | C2 | semidirect |
| 3. C4×#217 | C2 | semidirect |
| 4. C2×#825 | C2 | semidirect |
| 11. C2×#235 | C4 | semidirect |
| 13. C22×D12 | C4 | semidirect |
| 15. C22×Dic6 | C4 | semidirect |
| 16. C2×C3×M16 | C22 | semidirect |
| 18. C2×C4×Dic3 | C22 | semidirect |
| 25. #407 | D3 | semidirect |
| 70. C2×M16 | C2×D3 | semidirect |
| 106. D12 | C22⋊C4 | semidirect |
| 111. Dic6 | C22⋊C4 | semidirect |
| 154. C22×C3 | #104 | semidirect |
| 222. C22 | #825 | semidirect |
| 231. C3 | #1789 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#235 | 2 |
| C3×#407 | 2 |
| C4×#217 | 2 |
| C2×#825 | 2 |
| #1789 | 3 |