Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
500 conjugacy classes of subgroups; only the 185 normal subgroups are shown.
This group has 500 conjugacy classes of subgroups — too many to draw. Only its 185 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. #5522 | C2 | semidirect |
| 3. C3×#427 | C2 | semidirect |
| 4. C2×C8×Dic3 | C2 | semidirect |
| 5. #5002 | C2 | semidirect |
| 6. #4873 | C2 | semidirect |
| 7. #4872 | C2 | semidirect |
| 8. #4852 | C2 | semidirect |
| 16. #904 | C4 | semidirect |
| 35. #427 | D3 | semidirect |
| 42. #235 | C2×C4 | semidirect |
| 47. C2×C3×C8 | C2×C4 | semidirect |
| 61. Dic12 | C2×C4 | semidirect |
| 62. D24 | C2×C4 | semidirect |
| 63. #204 | C2×C4 | semidirect |
| 119. C2×C8 | C4×D3 | semidirect |
| 142. Dic3 | #135 | semidirect |
| 180. C3 | C4×#135 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#904 | 2 |
| #5522 | 2 |
| C3×#427 | 2 |
| C2×C8×Dic3 | 2 |
| #5002 | 2 |
| #4873 | 2 |
| #4872 | 2 |
| #4852 | 2 |
| C4×#135 | 3 |