Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
390 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 390 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 |
|---|---|---|
| 1. C2×D3×M16 | C2 | semidirect |
| 3. C2×#823 | C2 | semidirect |
| 4. C2×#823 | C2 | semidirect |
| 5. #5126 | C2 | semidirect |
| 6. C3×#343 | C2 | semidirect |
| 7. #4530 | C2 | semidirect |
| 36. #343 | D3 | semidirect |
| 62. C3×M16 | D4 | semidirect |
| 72. #208 | D4 | semidirect |
| 170. M16 | D12 | semidirect |
| 197. C2×D3 | #100 | semidirect |
| 280. C3 | #1900 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D3×M16 | 2 |
| C2×#895 | 2 |
| C2×#823 | 2 |
| #5126 | 2 |
| C3×#343 | 2 |
| #4530 | 2 |
| #1900 | 3 |