Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
236 conjugacy classes of subgroups; only the 77 normal subgroups are shown.
This group has 236 conjugacy classes of subgroups — too many to draw. Only its 77 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. D3×M32 | C2 | semidirect |
| 3. C3×#349 | C2 | semidirect |
| 4. #4553 | C2 | semidirect |
| 5. #4514 | C2 | semidirect |
| 16. C3×M32 | C22 | semidirect |
| 17. #812 | C22 | semidirect |
| 24. #349 | D3 | direct (N × H) |
| 61. M32 | C2×D3 | semidirect |
| 165. D3 | #349 | direct (N × H) |
| 182. C3 | C2×#349 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D3×M16 | 2 |
| D3×M32 | 2 |
| C3×#349 | 2 |
| #4553 | 2 |
| #4514 | 2 |
| C2×#349 | 3 |