Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
435 conjugacy classes of subgroups; only the 122 normal subgroups are shown.
This group has 435 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 |
|---|---|---|
| 5. #68723 | C3 | direct (N × H) |
| 131. C32 | #2070 | semidirect |
| 152. C3 | #68723 | direct (N × H) |
| 153. C3 | C3×#2070 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×#824 | 2 |
| C3×#5124 | 2 |
| C32×#338 | 2 |
| C3×#2070 | 3 |
| #68723 | 3 |