Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
312 conjugacy classes of subgroups; only the 98 normal subgroups are shown.
This group has 312 conjugacy classes of subgroups — too many to draw. Only its 98 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 |
|---|---|---|
| 9. #68515 | C3 | direct (N × H) |
| 264. C32 | #1704 | semidirect |
| 302. C3 | #68515 | direct (N × H) |
| 303. C3 | C3×#1704 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#5093 | 2 |
| C3×#5091 | 2 |
| C3×#4851 | 2 |
| C3×#4831 | 2 |
| C32×#333 | 2 |
| C3×#4482 | 2 |
| C3×#4480 | 2 |
| C3×#1704 | 3 |
| #68515 | 3 |