Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
636 conjugacy classes of subgroups; only the 181 normal subgroups are shown.
This group has 636 conjugacy classes of subgroups — too many to draw. Only its 181 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. #10589331 | C2 | semidirect |
| 180. C32 | #1531 | semidirect |
| 213. C3 | #69801 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10595941 | 2 |
| C2×C32×#97 | 2 |
| #10592625 | 2 |
| #10589331 | 2 |
| #69801 | 3 |