Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
273 conjugacy classes of subgroups; only the 110 normal subgroups are shown.
This group has 273 conjugacy classes of subgroups — too many to draw. Only its 110 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 |
|---|---|---|
| 4. C3×#4512 | C2 | semidirect |
| 5. C3×#4511 | C2 | semidirect |
| 7. #69115 | C3 | direct (N × H) |
| 26. #4512 | C2×C3 | semidirect |
| 27. #4511 | C2×C3 | semidirect |
| 193. C32 | #2166 | semidirect |
| 223. C3 | #69115 | direct (N × H) |
| 224. C3 | C3×#2166 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#5122 | 2 |
| C32×#349 | 2 |
| C3×#4553 | 2 |
| C3×#4512 | 2 |
| C3×#4511 | 2 |
| C3×#2166 | 3 |
| #69115 | 3 |