Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
760 conjugacy classes of subgroups; only the 165 normal subgroups are shown.
This group has 760 conjugacy classes of subgroups — too many to draw. Only its 165 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. C22×#214 | C2 | semidirect |
| 3. C22×Dic12 | C2 | semidirect |
| 4. C2×#897 | C2 | semidirect |
| 5. C2×C3×#102 | C2 | semidirect |
| 6. C2×(C2×D3)⋊C8 | C2 | semidirect |
| 7. C2×#810 | C2 | semidirect |
| 8. #4783 | C2 | direct (N × H) |
| 23. C2×#214 | C22 | semidirect |
| 28. C2×Dic12 | C22 | semidirect |
| 30. #897 | C22 | semidirect |
| 31. C3×#102 | C22 | semidirect |
| 32. (C2×D3)⋊C8 | C22 | semidirect |
| 33. #810 | C22 | semidirect |
| 40. C2×#102 | D3 | semidirect |
| 104. #102 | C2×D3 | semidirect |
| 240. C2×C3 | #452 | semidirect |
| 264. C3 | C2×#452 | semidirect |
| 267. C2 | #4783 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#237 | 2 |
| C22×#214 | 2 |
| C22×Dic12 | 2 |
| C2×#897 | 2 |
| C2×C3×#102 | 2 |
| C2×(C2×D3)⋊C8 | 2 |
| C2×#810 | 2 |
| #4783 | 2 |
| C2×#452 | 3 |