Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
472 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 472 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. C2×D3×Q16 | C2 | semidirect |
| 4. C3×#462 | C2 | semidirect |
| 5. #5186 | C2 | semidirect |
| 6. #5092 | C2 | semidirect |
| 7. C4×#216 | C2 | semidirect |
| 8. #4849 | C2 | semidirect |
| 10. #4813 | C2 | semidirect |
| 11. #4809 | C2 | semidirect |
| 49. #462 | D3 | semidirect |
| 78. #216 | D4 | semidirect |
| 139. D12 | Q16 | semidirect |
| 196. C2×D3 | C2×Q16 | semidirect |
| 201. C3×C4 | C2×Q16 | semidirect |
| 253. C4 | D3×Q16 | semidirect |
| 256. C3 | D4×Q16 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D3×Q16 | 2 |
| #5727 | 2 |
| Q8×D12 | 2 |
| C3×#462 | 2 |
| #5186 | 2 |
| #5092 | 2 |
| C4×#216 | 2 |
| #4849 | 2 |
| #4834 | 2 |
| #4813 | 2 |
| #4809 | 2 |
| D4×Q16 | 3 |