Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
860 conjugacy classes of subgroups; only the 236 normal subgroups are shown.
This group has 860 conjugacy classes of subgroups — too many to draw. Only its 236 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 |
|---|---|---|
| 31. C32×C3⋊C8 | Q8 | semidirect |
| 89. C3×C3⋊C8 | Dic6 | semidirect |
| 135. C33 | #500 | semidirect |
| 156. C3⋊C8 | #634 | semidirect |
| 192. C32 | #4682 | semidirect |
| 193. C32 | #5078 | semidirect |
| 218. C3 | #10590311 | semidirect |
| 219. C3 | #10592381 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11723910 | 2 |
| C3×#64078 | 2 |
| C32×C4×C3⋊C8 | 2 |
| #11722055 | 2 |
| #10592381 | 3 |
| #10590311 | 3 |