Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
756 conjugacy classes of subgroups; only the 197 normal subgroups are shown.
This group has 756 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. #10589322 | C2 | semidirect |
| 78. #634 | M16 | semidirect |
| 189. C32 | #1491 | semidirect |
| 225. C3 | #69857 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×#634 | 2 |
| C32×C4×M16 | 2 |
| #10592625 | 2 |
| #10589322 | 2 |
| #69857 | 3 |