Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
277 conjugacy classes of subgroups; only the 98 normal subgroups are shown.
This group has 277 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. #69212 | C3 | direct (N × H) |
| 224. C32 | #2229 | semidirect |
| 256. C3 | #69212 | direct (N × H) |
| 257. C3 | C3×#2229 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×Dic3×Q16 | 2 |
| C3×#4878 | 2 |
| C32×#358 | 2 |
| C3×#4564 | 2 |
| C3×#4505 | 2 |
| C3×Dic3⋊C16 | 2 |
| C3×#4489 | 2 |
| C3×#2229 | 3 |
| #69212 | 3 |