Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
475 conjugacy classes of subgroups; only the 122 normal subgroups are shown.
This group has 475 conjugacy classes of subgroups — too many to draw. Only its 122 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. C3×#5124 | C2 | semidirect |
| 3. C32×#338 | C2 | semidirect |
| 5. #68722 | C3 | direct (N × H) |
| 14. #5124 | C2×C3 | semidirect |
| 16. C3×#338 | D3 | semidirect |
| 17. C3×#338 | C2×C3 | semidirect |
| 51. #338 | C3×D3 | semidirect |
| 138. C32 | #2069 | semidirect |
| 163. C3 | #68722 | direct (N × H) |
| 164. C3 | C3×#2069 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×#823 | 2 |
| C3×#5124 | 2 |
| C32×#338 | 2 |
| C3×#2069 | 3 |
| #68722 | 3 |