Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
482 conjugacy classes of subgroups; only the 131 normal subgroups are shown.
This group has 482 conjugacy classes of subgroups — too many to draw. Only its 131 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×#919 | C2 | semidirect |
| 2. C2×D3×Q16 | C2 | semidirect |
| 3. #5576 | C2 | semidirect |
| 4. C3×C4×Q16 | C2 | semidirect |
| 5. #5028 | C2 | semidirect |
| 6. #4887 | C2 | semidirect |
| 7. #4883 | C2 | semidirect |
| 8. #4808 | C2 | semidirect |
| 9. #4806 | C2 | semidirect |
| 10. #4696 | C2 | semidirect |
| 11. C8×D12 | C2 | semidirect |
| 51. C4×Q16 | D3 | semidirect |
| 68. C3×Q16 | D4 | semidirect |
| 169. Q16 | D12 | semidirect |
| 200. C2×D3 | #135 | semidirect |
| 266. C3 | #3285 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#919 | 2 |
| C2×D3×Q16 | 2 |
| #5576 | 2 |
| C3×C4×Q16 | 2 |
| #5028 | 2 |
| #4887 | 2 |
| #4883 | 2 |
| #4808 | 2 |
| #4806 | 2 |
| #4696 | 2 |
| C8×D12 | 2 |
| #3285 | 3 |