Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
592 conjugacy classes of subgroups; only the 181 normal subgroups are shown.
This group has 592 conjugacy classes of subgroups — too many to draw. Only its 181 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×#204 | C2 | semidirect |
| 4. C2×#875 | C2 | semidirect |
| 5. C2×C3×C4×C8 | C2 | semidirect |
| 6. #4696 | C2 | direct (N × H) |
| 15. C2×Dic12 | C22 | semidirect |
| 19. C2×#204 | C22 | semidirect |
| 21. #875 | C22 | semidirect |
| 22. C3×C4×C8 | C22 | semidirect |
| 28. C2×C4×C8 | D3 | semidirect |
| 65. C4×C8 | C2×D3 | semidirect |
| 139. C2×C3 | #495 | semidirect |
| 154. C3 | C2×#495 | semidirect |
| 156. C2 | #4696 | 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×#204 | 2 |
| C2×#875 | 2 |
| C2×C3×C4×C8 | 2 |
| #4696 | 2 |
| C2×#495 | 3 |