Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
323 conjugacy classes of subgroups; only the 118 normal subgroups are shown.
This group has 323 conjugacy classes of subgroups — too many to draw. Only its 118 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 |
|---|---|---|
| 7. #69318 | C3 | direct (N × H) |
| 15. C3×Dic24 | C4 | semidirect |
| 56. Dic24 | C3×C4 | semidirect |
| 103. C3×Dic3 | Q32 | semidirect |
| 167. Dic3 | C3×Q32 | semidirect |
| 168. C32 | C4×Q32 | semidirect |
| 196. C3 | #69318 | direct (N × H) |
| 197. C3 | C3×C4×Q32 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×Dic24 | 2 |
| C3×#4873 | 2 |
| C32×#366 | 2 |
| C3×Dic3×C16 | 2 |
| C3×#4492 | 2 |
| C3×C4×Q32 | 3 |
| #69318 | 3 |