Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
504 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 504 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×#919 | C2 | semidirect |
| 2. #5577 | C2 | semidirect |
| 3. C3×C4×Q16 | C2 | semidirect |
| 4. #5027 | C2 | semidirect |
| 5. #4883 | C2 | semidirect |
| 6. #4810 | C2 | semidirect |
| 7. #4695 | C2 | semidirect |
| 8. C8×D12 | C2 | semidirect |
| 36. C4×Q16 | D3 | semidirect |
| 49. C3×Q16 | D4 | semidirect |
| 118. Q16 | D12 | semidirect |
| 143. C3×C4 | #135 | semidirect |
| 186. C4 | #919 | semidirect |
| 189. C3 | #3287 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#919 | 2 |
| #5577 | 2 |
| C3×C4×Q16 | 2 |
| #5027 | 2 |
| #4883 | 2 |
| #4810 | 2 |
| #4695 | 2 |
| C8×D12 | 2 |
| #3287 | 3 |