Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
443 conjugacy classes of subgroups; only the 186 normal subgroups are shown.
This group has 443 conjugacy classes of subgroups — too many to draw. Only its 186 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. #68717 | C3 | direct (N × H) |
| 9. C3×#815 | C4 | semidirect |
| 10. C3×C8×Dic3 | C4 | semidirect |
| 36. #815 | C3×C4 | semidirect |
| 37. C8×Dic3 | C3×C4 | semidirect |
| 119. C32 | #1747 | semidirect |
| 139. C3 | #68717 | direct (N × H) |
| 140. C3 | C3×#1747 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#5122 | 2 |
| C32×#338 | 2 |
| C3×#4557 | 2 |
| C3×#1747 | 3 |
| #68717 | 3 |