Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
828 conjugacy classes of subgroups; only the 261 normal subgroups are shown.
This group has 828 conjugacy classes of subgroups — too many to draw. Only its 261 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 |
|---|---|---|
| 11. C2×C32×Q16 | C4 | semidirect |
| 54. C2×C3×Q16 | Dic3 | semidirect |
| 125. C2×Q16 | C3⋊Dic3 | semidirect |
| 191. C32 | #1979 | semidirect |
| 225. C3 | #72069 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C32×Q16 | 2 |
| C2×#63663 | 2 |
| #10592924 | 2 |
| C2×#63646 | 2 |
| #10592800 | 2 |
| #72069 | 3 |