Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
442 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 442 conjugacy classes of subgroups — too many to draw. Only its 97 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. C22×C4×Dic3 | C2 | semidirect |
| 3. C3×#407 | C2 | semidirect |
| 4. C2×#825 | C2 | semidirect |
| 5. #4555 | C2 | semidirect |
| 12. #930 | C4 | semidirect |
| 16. #924 | C4 | semidirect |
| 25. #407 | D3 | semidirect |
| 41. C2×D12 | C2×C4 | semidirect |
| 43. C2×Dic6 | C2×C4 | semidirect |
| 50. C4⋊Dic3 | C2×C4 | semidirect |
| 55. C4×Dic3 | D4 | semidirect |
| 132. C22×C3 | #104 | semidirect |
| 184. C22 | #825 | semidirect |
| 194. C3 | #1896 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #5791 | 2 |
| C22×C4×Dic3 | 2 |
| C3×#407 | 2 |
| C2×#825 | 2 |
| #4555 | 2 |
| #1896 | 3 |