Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
376 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 376 conjugacy classes of subgroups — too many to draw. Only its 85 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×D3×M16 | C2 | semidirect |
| 3. C2×C3×#104 | C2 | semidirect |
| 4. C2×#837 | C2 | semidirect |
| 5. C4×(C2×D3)⋊C4 | C2 | semidirect |
| 6. #4555 | C2 | semidirect |
| 7. #4523 | C2 | semidirect |
| 13. #946 | C4 | semidirect |
| 14. #946 | C4 | semidirect |
| 15. #938 | C4 | semidirect |
| 16. #938 | C4 | semidirect |
| 35. C2×#104 | D3 | semidirect |
| 63. C3×M16 | D4 | semidirect |
| 81. #208 | D4 | semidirect |
| 182. M16 | #67 | semidirect |
| 216. C2×D3 | #104 | semidirect |
| 310. C3 | #1871 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #5828 | 2 |
| C2×D3×M16 | 2 |
| C2×C3×#104 | 2 |
| C2×#837 | 2 |
| C4×(C2×D3)⋊C4 | 2 |
| #4555 | 2 |
| #4523 | 2 |
| #1871 | 3 |