Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
169 conjugacy classes of subgroups; only the 69 normal subgroups are shown.
This group has 169 conjugacy classes of subgroups — too many to draw. Only its 69 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 |
|---|---|---|
| 20. #3771 | Q8 | semidirect |
| 32. #634 | C16 | semidirect |
| 89. C32 | Q8×C16 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10593750 | 2 |
| #10593265 | 2 |
| C4⋊#3771 | 2 |
| C4×#3771 | 2 |
| Q8×C16 | 9 |