Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
468 conjugacy classes of subgroups; only the 161 normal subgroups are shown.
This group has 468 conjugacy classes of subgroups — too many to draw. Only its 161 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 |
|---|---|---|
| 60. C32×C8 | Q16 | semidirect |
| 112. C3×C8 | #216 | semidirect |
| 139. C32 | #1674 | semidirect |
| 153. C8 | #3756 | semidirect |
| 166. C3 | #70944 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C32×C8×Q8 | 2 |
| #10592730 | 2 |
| #10592381 | 2 |
| #10589352 | 2 |
| #10589324 | 2 |
| #70944 | 3 |