Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
265 conjugacy classes of subgroups; only the 78 normal subgroups are shown.
This group has 265 conjugacy classes of subgroups — too many to draw. Only its 78 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. #67528 | C3 | direct (N × H) |
| 9. C2×C3×Dic12 | C4 | semidirect |
| 11. C3×#818 | C4 | semidirect |
| 42. C2×Dic12 | C3×C4 | semidirect |
| 48. #818 | C3×C4 | semidirect |
| 199. C32 | #1348 | semidirect |
| 241. C3 | #67528 | direct (N × H) |
| 242. C3 | C3×#1348 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#5116 | 2 |
| C32×C22⋊C16 | 2 |
| C3×#4551 | 2 |
| C3×#1348 | 3 |
| #67528 | 3 |