Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
416 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 416 conjugacy classes of subgroups — too many to draw. Only its 141 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 |
|---|---|---|
| 3. C2×C3×#106 | C2 | semidirect |
| 5. C2×#816 | C2 | semidirect |
| 6. C2×#810 | C2 | semidirect |
| 7. C2×#807 | C2 | semidirect |
| 8. #4868 | C2 | direct (N × H) |
| 25. C3×#106 | C22 | semidirect |
| 27. #816 | C22 | semidirect |
| 28. #810 | C22 | semidirect |
| 29. #807 | C22 | semidirect |
| 34. C2×#106 | D3 | semidirect |
| 83. #106 | C2×D3 | semidirect |
| 186. C2×C3 | #485 | semidirect |
| 207. C3 | C2×#485 | semidirect |
| 209. C2 | #4868 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#897 | 2 |
| C2×#892 | 2 |
| C2×C3×#106 | 2 |
| C2×(C2×D3)⋊C8 | 2 |
| C2×#816 | 2 |
| C2×#810 | 2 |
| C2×#807 | 2 |
| #4868 | 2 |
| C2×#485 | 3 |