Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
360 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 360 conjugacy classes of subgroups — too many to draw. Only its 133 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. C2×C3×M32 | C2 | semidirect |
| 4. #4909 | C2 | direct (N × H) |
| 5. C2×Dic24 | C2 | semidirect |
| 6. C2×#800 | C2 | semidirect |
| 15. C2×Dic12 | C22 | semidirect |
| 20. C3×M32 | C22 | semidirect |
| 22. Dic24 | C22 | semidirect |
| 23. #800 | C22 | semidirect |
| 29. C2×M32 | D3 | semidirect |
| 69. M32 | C2×D3 | semidirect |
| 149. C2×C3 | #510 | semidirect |
| 162. C3 | C2×#510 | semidirect |
| 165. C2 | #4909 | 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 |
| C2×#904 | 2 |
| C2×C3×M32 | 2 |
| #4909 | 2 |
| C2×Dic24 | 2 |
| C2×#800 | 2 |
| C2×#510 | 3 |