Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
274 conjugacy classes of subgroups; only the 66 normal subgroups are shown.
This group has 274 conjugacy classes of subgroups — too many to draw. Only its 66 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 |
|---|---|---|
| 28. #3746 | C8 | semidirect |
| 45. #622 | Q16 | semidirect |
| 111. C32 | C8×Q16 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10593750 | 2 |
| #10592572 | 2 |
| #10590171 | 2 |
| C8×#622 | 2 |
| #10590161 | 2 |
| C8×Q16 | 9 |