Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
569 conjugacy classes of subgroups; only the 212 normal subgroups are shown.
This group has 569 conjugacy classes of subgroups — too many to draw. Only its 212 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 |
|---|---|---|
| 12. C3×#803 | C4 | semidirect |
| 13. C3×C4×C3⋊C8 | C4 | semidirect |
| 49. #803 | Dic3 | semidirect |
| 50. C4×C3⋊C8 | Dic3 | semidirect |
| 167. C32 | #1746 | semidirect |
| 195. C3 | #69751 | semidirect |
| 196. C3 | #69806 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10592631 | 2 |
| C2×C3×#803 | 2 |
| C2×C3×C4×C3⋊C8 | 2 |
| #10589156 | 2 |
| #69806 | 3 |
| #69751 | 3 |