Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
420 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 420 conjugacy classes of subgroups — too many to draw. Only its 125 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 |
|---|---|---|
| 2. Q8×D12 | C2 | semidirect |
| 3. C3×#475 | C2 | semidirect |
| 4. #5093 | C2 | semidirect |
| 5. C4×#215 | C2 | semidirect |
| 6. #4864 | C2 | semidirect |
| 7. #4862 | C2 | semidirect |
| 8. #4841 | C2 | semidirect |
| 9. #4834 | C2 | semidirect |
| 10. #4806 | C2 | semidirect |
| 11. D3×#103 | C2 | semidirect |
| 46. #475 | D3 | semidirect |
| 122. C3×Q8 | #41 | semidirect |
| 135. D12 | SD16 | semidirect |
| 207. Q8 | #239 | semidirect |
| 251. C3 | #3298 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #5726 | 2 |
| Q8×D12 | 2 |
| C3×#475 | 2 |
| #5093 | 2 |
| C4×#215 | 2 |
| #4864 | 2 |
| #4862 | 2 |
| #4841 | 2 |
| #4834 | 2 |
| #4806 | 2 |
| D3×#103 | 2 |
| #3298 | 3 |