Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
564 conjugacy classes of subgroups; only the 281 normal subgroups are shown.
This group has 564 conjugacy classes of subgroups — too many to draw. Only its 281 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 |
|---|---|---|
| 92. C32 | #1837 | semidirect |
| 112. C3 | #69791 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C32×C4×C8 | 2 |
| #10592623 | 2 |
| #10589418 | 2 |
| #69791 | 3 |