Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
307 conjugacy classes of subgroups; only the 86 normal subgroups are shown.
This group has 307 conjugacy classes of subgroups — too many to draw. Only its 86 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 |
| 5. C32×#362 | C2 | semidirect |
| 6. C3×#4517 | C2 | semidirect |
| 7. C3×#4493 | C2 | semidirect |
| 9. #69270 | C3 | direct (N × H) |
| 30. C2×#829 | C2×C3 | semidirect |
| 36. C3×#362 | D3 | semidirect |
| 37. C3×#362 | C2×C3 | semidirect |
| 38. #4517 | C2×C3 | semidirect |
| 39. #4493 | C2×C3 | semidirect |
| 116. #362 | C3×D3 | semidirect |
| 265. C32 | #2222 | semidirect |
| 298. C3 | #69270 | direct (N × H) |
| 299. C3 | C3×#2222 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#5192 | 2 |
| C2×C3×#829 | 2 |
| C3×#4907 | 2 |
| C3×#4896 | 2 |
| C32×#362 | 2 |
| C3×#4517 | 2 |
| C3×#4493 | 2 |
| C3×#2222 | 3 |
| #69270 | 3 |