Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
120 conjugacy classes of subgroups; only the 66 normal subgroups are shown.
This group has 120 conjugacy classes of subgroups — too many to draw. Only its 66 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. #67601 | C3 | direct (N × H) |
| 9. C32×C32 | C4 | semidirect |
| 31. C3×C32 | Dic3 | semidirect |
| 32. C3×C32 | C3×C4 | semidirect |
| 61. C32 | C3×Dic3 | semidirect |
| 93. C32 | #1426 | semidirect |
| 110. C3 | #67601 | direct (N × H) |
| 111. C3 | C3×#1426 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C32×M64 | 2 |
| C3×#4506 | 2 |
| C3×#4505 | 2 |
| C3×#1426 | 3 |
| #67601 | 3 |