Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
388 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 388 conjugacy classes of subgroups — too many to draw. Only its 101 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×#95 | C2 | semidirect |
| 3. C2×#830 | C2 | semidirect |
| 4. #4451 | C2 | direct (N × H) |
| 9. C22×D12 | C4 | semidirect |
| 12. #930 | C4 | semidirect |
| 15. C2×C4⋊Dic3 | C4 | semidirect |
| 18. C3×#95 | C22 | semidirect |
| 20. #830 | C22 | semidirect |
| 23. C2×#95 | D3 | semidirect |
| 45. C2×D12 | C2×C4 | semidirect |
| 49. C4⋊Dic3 | C2×C4 | semidirect |
| 66. #95 | C2×D3 | semidirect |
| 186. C2×C3 | #327 | semidirect |
| 214. C3 | C2×#327 | semidirect |
| 219. C2 | #4451 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#930 | 2 |
| C2×C3×#95 | 2 |
| C2×#830 | 2 |
| #4451 | 2 |
| C2×#327 | 3 |