Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
296 conjugacy classes of subgroups; only the 90 normal subgroups are shown.
This group has 296 conjugacy classes of subgroups — too many to draw. Only its 90 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 |
|---|---|---|
| 3. C3×#2916 | C3 | semidirect |
| 4. #2916⋊C3 | C3 | direct (N × H) |
| 21. #2916 | C32 | semidirect |
| 172. C3 | #2916⋊C3 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#568⋊C3 | 2 |
| C2×C3×#131⋊C3 | 2 |
| C3×#2916 | 3 |
| #2916⋊C3 | 3 |
| C32×#108 | 4 |