Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
450 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 450 conjugacy classes of subgroups — too many to draw. Only its 149 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 |
|---|---|---|
| 179. C32 | #1680 | semidirect |
| 211. C3 | #70946 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C32×C8×Q8 | 2 |
| #10592730 | 2 |
| #10592719 | 2 |
| #10592380 | 2 |
| #10589352 | 2 |
| #10589348 | 2 |
| #10589323 | 2 |
| #70946 | 3 |