Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
450 conjugacy classes of subgroups; only the 157 normal subgroups are shown.
This group has 450 conjugacy classes of subgroups — too many to draw. Only its 157 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 |
|---|---|---|
| 16. #63656 | C4 | direct (N × H) |
| 100. C32×C4 | Q32 | semidirect |
| 155. C3×C4 | #829 | semidirect |
| 160. C32 | C4×Q32 | semidirect |
| 184. C4 | #63656 | direct (N × H) |
| 187. C3 | C4×#829 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C32×C4×Q16 | 2 |
| C2×#63656 | 2 |
| C4×#3746 | 2 |
| #10589430 | 2 |
| #10589358 | 2 |
| #10589355 | 2 |
| C4×C3⋊(C3⋊C16) | 2 |
| C4×#829 | 3 |