Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
848 conjugacy classes of subgroups; only the 192 normal subgroups are shown.
This group has 848 conjugacy classes of subgroups — too many to draw. Only its 192 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 |
|---|---|---|
| 36. C3×#634 | Q8 | semidirect |
| 99. #634 | Dic6 | semidirect |
| 159. C33 | #477 | semidirect |
| 226. C32 | #4850 | semidirect |
| 227. C32 | #5021 | semidirect |
| 256. C3 | #10590283 | semidirect |
| 257. C3 | #10592549 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11723910 | 2 |
| C3×C4×#634 | 2 |
| C32×C4⋊(C3⋊C8) | 2 |
| #11722055 | 2 |
| #11722040 | 2 |
| #10592549 | 3 |
| #10590283 | 3 |