Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
203 conjugacy classes of subgroups; only the 46 normal subgroups are shown.
This group has 203 conjugacy classes of subgroups — too many to draw. Only its 46 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 |
|---|---|---|
| 5. #67543 | C3 | direct (N × H) |
| 7. C3×#870 | C4 | semidirect |
| 12. C3×C4×C3⋊C8 | C4 | semidirect |
| 34. #870 | C3×C4 | semidirect |
| 45. C4×C3⋊C8 | C3×C4 | semidirect |
| 159. C32 | #1414 | semidirect |
| 188. C3 | #67543 | direct (N × H) |
| 189. C3 | C3×#1414 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#5056 | 2 |
| C32×#354 | 2 |
| C3×#4542 | 2 |
| C3×#1414 | 3 |
| #67543 | 3 |