Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
702 conjugacy classes of subgroups; only the 197 normal subgroups are shown.
This group has 702 conjugacy classes of subgroups — too many to draw. Only its 197 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 |
|---|---|---|
| 4. #10589405 | C2 | semidirect |
| 7. C22×C32×Q8 | C4 | semidirect |
| 10. C32×#123 | C4 | semidirect |
| 14. C32×#117 | C4 | semidirect |
| 54. C22×C3×Q8 | Dic3 | semidirect |
| 57. C3×#123 | Dic3 | semidirect |
| 61. C3×#117 | Dic3 | semidirect |
| 140. C22×Q8 | C3⋊Dic3 | semidirect |
| 144. #123 | C3⋊Dic3 | semidirect |
| 149. #117 | C3⋊Dic3 | semidirect |
| 226. C32 | #2123 | semidirect |
| 272. C3 | #71870 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C32×#536 | 2 |
| #10592939 | 2 |
| #10592936 | 2 |
| #10589405 | 2 |
| #71870 | 3 |