Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
426 conjugacy classes of subgroups; only the 139 normal subgroups are shown.
This group has 426 conjugacy classes of subgroups — too many to draw. Only its 139 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. #5577 | C2 | semidirect |
| 2. Q8×D12 | C2 | semidirect |
| 3. C3×C8×Q8 | C2 | semidirect |
| 4. #4846 | C2 | semidirect |
| 5. #4843 | C2 | semidirect |
| 6. #4694 | C2 | semidirect |
| 7. C4×D24 | C2 | semidirect |
| 30. C8×Q8 | D3 | semidirect |
| 70. C3×Q8 | D8 | semidirect |
| 81. D12 | #41 | semidirect |
| 123. Q8 | D24 | semidirect |
| 157. C3 | #3358 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #5577 | 2 |
| Q8×D12 | 2 |
| C3×C8×Q8 | 2 |
| #4846 | 2 |
| #4843 | 2 |
| #4694 | 2 |
| C4×D24 | 2 |
| #3358 | 3 |