Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
400 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 400 conjugacy classes of subgroups — too many to draw. Only its 149 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 |
|---|---|---|
| 1. C22×Dic12 | C2 | semidirect |
| 3. C22×C3×C16 | C2 | semidirect |
| 4. C2×#800 | C2 | direct (N × H) |
| 10. C2×Dic12 | C22 | semidirect |
| 13. C2×C3×C16 | C22 | semidirect |
| 14. #800 | C22 | direct (N × H) |
| 18. C22×C16 | D3 | semidirect |
| 29. Dic12 | C23 | semidirect |
| 32. C3×C16 | C23 | semidirect |
| 41. C2×C16 | C2×D3 | semidirect |
| 67. C16 | C22×D3 | semidirect |
| 68. C22×C3 | SD32 | semidirect |
| 87. C2×C3 | C2×SD32 | semidirect |
| 92. C22 | #800 | direct (N × H) |
| 97. C3 | C22×SD32 | semidirect |
| 99. C2 | C2×#800 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×Dic12 | 2 |
| C22×D24 | 2 |
| C22×C3×C16 | 2 |
| C2×#800 | 2 |
| C22×SD32 | 3 |