Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
416 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 416 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. D3×C4⋊Q8 | C2 | semidirect |
| 3. C3×#475 | C2 | semidirect |
| 4. #5087 | C2 | semidirect |
| 5. #5020 | C2 | semidirect |
| 6. #4870 | C2 | semidirect |
| 7. #4861 | C2 | semidirect |
| 8. #4846 | C2 | semidirect |
| 9. #4837 | C2 | semidirect |
| 11. #4793 | C2 | semidirect |
| 49. #475 | D3 | semidirect |
| 58. #239 | Q8 | semidirect |
| 129. C3×Q8 | C2×Q8 | semidirect |
| 143. D12 | C2×Q8 | semidirect |
| 220. Q8 | D3×Q8 | semidirect |
| 269. C3 | #3079 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D3×C4⋊Q8 | 2 |
| C4×#239 | 2 |
| C3×#475 | 2 |
| #5087 | 2 |
| #5020 | 2 |
| #4870 | 2 |
| #4861 | 2 |
| #4846 | 2 |
| #4837 | 2 |
| #4803 | 2 |
| #4793 | 2 |
| #3079 | 3 |