Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
189 conjugacy classes of subgroups; only the 74 normal subgroups are shown.
This group has 189 conjugacy classes of subgroups — too many to draw. Only its 74 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. #67826 | C3 | direct (N × H) |
| 8. C32×Q32 | C4 | semidirect |
| 34. C3×Q32 | Dic3 | semidirect |
| 35. C3×Q32 | C3×C4 | semidirect |
| 80. Q32 | C3×Dic3 | semidirect |
| 128. C32 | #1416 | semidirect |
| 151. C3 | #67826 | direct (N × H) |
| 152. C3 | C3×#1416 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C32×Q32 | 2 |
| C3×#4504 | 2 |
| C2×C3×C3⋊C32 | 2 |
| C3×#1416 | 3 |
| #67826 | 3 |