Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
305 conjugacy classes of subgroups; only the 94 normal subgroups are shown.
This group has 305 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 |
|---|---|---|
| 2. C3×#4878 | C2 | semidirect |
| 3. C32×#358 | C2 | semidirect |
| 4. C3×#4564 | C2 | semidirect |
| 6. C3×Dic3×C16 | C2 | semidirect |
| 9. #69216 | C3 | direct (N × H) |
| 24. #4878 | C2×C3 | semidirect |
| 27. C3×#358 | D3 | semidirect |
| 28. C3×#358 | C2×C3 | semidirect |
| 32. #4564 | C2×C3 | semidirect |
| 34. Dic3×C16 | C2×C3 | semidirect |
| 97. #358 | C3×D3 | semidirect |
| 249. C32 | #2242 | semidirect |
| 287. C3 | #69216 | direct (N × H) |
| 288. C3 | C3×#2242 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#5191 | 2 |
| C3×#4878 | 2 |
| C32×#358 | 2 |
| C3×#4564 | 2 |
| C3×#4509 | 2 |
| C3×Dic3×C16 | 2 |
| C3×#4491 | 2 |
| C3×#2242 | 3 |
| #69216 | 3 |