Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
306 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 306 conjugacy classes of subgroups — too many to draw. Only its 89 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 |
|---|---|---|
| 4. #11720235 | C2 | direct (N × H) |
| 94. C2×C3×C9 | Q32 | semidirect |
| 134. C3×C9 | C2×Q32 | semidirect |
| 163. C2×C9 | #829 | semidirect |
| 189. C9 | C2×#829 | semidirect |
| 201. C2×C3 | Dic72 | semidirect |
| 211. C3 | C2×Dic72 | semidirect |
| 213. C2 | #11720235 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#88521 | 2 |
| C2×C3×Dic36 | 2 |
| C2×C9×C3⋊C16 | 2 |
| #11720235 | 2 |
| C2×#63551 | 3 |
| C2×Dic72 | 3 |