Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
242 conjugacy classes of subgroups; only the 52 normal subgroups are shown.
This group has 242 conjugacy classes of subgroups — too many to draw. Only its 52 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 |
|---|---|---|
| 26. #6308 | Q8 | semidirect |
| 28. C32×Dic6 | Q8 | semidirect |
| 109. C33 | #475 | semidirect |
| 125. Dic6 | PSU(3,𝔽2) | semidirect |
| 161. C32 | #4851 | semidirect |
| 191. C3 | #10593561 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11724365 | 2 |
| Dic6×#157 | 2 |
| #11722806 | 2 |
| C3×#63744 | 2 |
| #11722709 | 2 |
| #10593561 | 3 |
| #4851 | 9 |