Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
461 conjugacy classes of subgroups; only the 106 normal subgroups are shown.
This group has 461 conjugacy classes of subgroups — too many to draw. Only its 106 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. C2×C3×#829 | C2 | semidirect |
| 3. C2×C3×Dic24 | C2 | semidirect |
| 5. C32×#358 | C2 | semidirect |
| 7. C3×#4492 | C2 | semidirect |
| 9. #69225 | C3 | direct (N × H) |
| 30. C2×#829 | C2×C3 | semidirect |
| 31. C2×Dic24 | C2×C3 | semidirect |
| 35. C3×#358 | D3 | semidirect |
| 36. C3×#358 | C2×C3 | semidirect |
| 39. #4492 | C2×C3 | semidirect |
| 123. #358 | C3×D3 | semidirect |
| 182. C2×C3×D3 | Q32 | semidirect |
| 288. C2×D3 | C3×Q32 | semidirect |
| 307. C32 | #2188 | semidirect |
| 351. C3 | #69225 | direct (N × H) |
| 352. C3 | C3×#2188 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×D3×Q16 | 2 |
| C2×C3×#829 | 2 |
| C2×C3×Dic24 | 2 |
| C3×#4887 | 2 |
| C32×#358 | 2 |
| C3×(C2×D3)⋊C16 | 2 |
| C3×#4492 | 2 |
| C3×#2188 | 3 |
| #69225 | 3 |