Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
295 conjugacy classes of subgroups; only the 94 normal subgroups are shown.
This group has 295 conjugacy classes of subgroups — too many to draw. Only its 94 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 |
|---|---|---|
| 1. C3×#4878 | C2 | semidirect |
| 3. C32×#366 | C2 | semidirect |
| 5. C3×Dic3⋊C16 | C2 | semidirect |
| 7. C3×#4490 | C2 | semidirect |
| 9. #69334 | C3 | direct (N × H) |
| 23. #4878 | C2×C3 | semidirect |
| 27. C3×#366 | D3 | semidirect |
| 28. C3×#366 | C2×C3 | semidirect |
| 33. Dic3⋊C16 | C2×C3 | semidirect |
| 35. #4490 | C2×C3 | semidirect |
| 93. #366 | C3×D3 | semidirect |
| 230. C32 | #2228 | semidirect |
| 267. C3 | #69334 | direct (N × H) |
| 268. C3 | C3×#2228 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#4878 | 2 |
| C3×#4872 | 2 |
| C32×#366 | 2 |
| C3×#4509 | 2 |
| C3×Dic3⋊C16 | 2 |
| C3×#4491 | 2 |
| C3×#4490 | 2 |
| C3×#2228 | 3 |
| #69334 | 3 |