Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
232 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 232 conjugacy classes of subgroups — too many to draw. Only its 85 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×C3×M32 | C2 | semidirect |
| 3. C2×#817 | C2 | semidirect |
| 4. #4518 | C2 | direct (N × H) |
| 9. C2×Dic12 | C4 | semidirect |
| 12. #904 | C4 | semidirect |
| 14. C2×D24 | C4 | semidirect |
| 17. C3×M32 | C22 | semidirect |
| 20. #817 | C22 | semidirect |
| 22. C2×M32 | D3 | semidirect |
| 44. Dic12 | C2×C4 | semidirect |
| 46. D24 | C2×C4 | semidirect |
| 61. M32 | C2×D3 | semidirect |
| 150. C2×C3 | #360 | semidirect |
| 165. C3 | C2×#360 | semidirect |
| 169. C2 | #4518 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#904 | 2 |
| C2×C3×M32 | 2 |
| C2×#817 | 2 |
| #4518 | 2 |
| C2×#360 | 3 |