Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
450 conjugacy classes of subgroups; only the 167 normal subgroups are shown.
This group has 450 conjugacy classes of subgroups — too many to draw. Only its 167 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 |
|---|---|---|
| 9. C32×Q32 | C4 | semidirect |
| 34. C3×Q32 | Dic3 | semidirect |
| 72. C3⋊Dic3 | Q32 | direct (N × H) |
| 75. Q32 | C3⋊Dic3 | direct (N × H) |
| 112. C32 | C4×Q32 | semidirect |
| 133. C3 | Dic3×Q32 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C32×Q32 | 2 |
| Q16×C3⋊Dic3 | 2 |
| #10589430 | 2 |
| #10589370 | 2 |
| C16×C3⋊Dic3 | 2 |
| Dic3×Q32 | 3 |