Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
350 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 350 conjugacy classes of subgroups — too many to draw. Only its 113 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. #5766 | C2 | semidirect |
| 2. C2×C3×Q32 | C2 | semidirect |
| 3. #5179 | C2 | semidirect |
| 4. #4919 | C2 | semidirect |
| 5. #4918 | C2 | semidirect |
| 6. D3×Q32 | C2 | semidirect |
| 7. #4904 | C2 | semidirect |
| 8. #4901 | C2 | semidirect |
| 35. C2×Q32 | D3 | semidirect |
| 158. C3 | #3417 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #5766 | 2 |
| C2×C3×Q32 | 2 |
| #5179 | 2 |
| #4919 | 2 |
| #4918 | 2 |
| D3×Q32 | 2 |
| #4904 | 2 |
| #4901 | 2 |
| #3417 | 3 |