Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
486 conjugacy classes of subgroups; only the 157 normal subgroups are shown.
This group has 486 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. #63642 | C4 | semidirect |
| 17. C8×C3⋊Dic3 | C4 | semidirect |
| 180. C32 | #1841 | semidirect |
| 213. C3 | #69017 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| M16×C3⋊Dic3 | 2 |
| C32×#344 | 2 |
| #10589426 | 2 |
| #10589422 | 2 |
| #10589421 | 2 |
| #10589398 | 2 |
| #10589397 | 2 |
| #69017 | 3 |