Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
353 conjugacy classes of subgroups; only the 96 normal subgroups are shown.
This group has 353 conjugacy classes of subgroups — too many to draw. Only its 96 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 |
|---|---|---|
| 80. C32×C8 | Q16 | semidirect |
| 169. C3×C8 | Dic12 | semidirect |
| 170. C3×C8 | #216 | semidirect |
| 211. C32 | #1694 | semidirect |
| 224. C8 | #3719 | semidirect |
| 243. C3 | #68552 | semidirect |
| 244. C3 | #70964 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10592381 | 2 |
| C3×#4679 | 2 |
| #10590385 | 2 |
| C3×#4457 | 2 |
| #10589094 | 2 |
| #70964 | 3 |
| #68552 | 3 |