Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
728 conjugacy classes of subgroups; only the 192 normal subgroups are shown.
This group has 728 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 |
|---|---|---|
| 34. C3×#634 | Q8 | semidirect |
| 93. #634 | Dic6 | semidirect |
| 153. C33 | #477 | semidirect |
| 218. C32 | #5021 | semidirect |
| 219. C32 | #5091 | semidirect |
| 248. C3 | #10590310 | semidirect |
| 249. C3 | #10592790 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C4×#634 | 2 |
| C32×#869 | 2 |
| C4⋊(C3⋊(C3⋊(C3⋊C8))) | 2 |
| #11722056 | 2 |
| #11722039 | 2 |
| #10592790 | 3 |
| #10590310 | 3 |