Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
450 conjugacy classes of subgroups; only the 127 normal subgroups are shown.
This group has 450 conjugacy classes of subgroups — too many to draw. Only its 127 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 | semidirect |
| 104. C3⋊Dic3 | Q32 | semidirect |
| 160. C32 | C4×Q32 | semidirect |
| 187. C3 | #69207 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q16×C3⋊Dic3 | 2 |
| C2×#63656 | 2 |
| #10592572 | 2 |
| C32×#358 | 2 |
| #10589369 | 2 |
| C16×C3⋊Dic3 | 2 |
| #10589355 | 2 |
| #69207 | 3 |