Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
326 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 326 conjugacy classes of subgroups — too many to draw. Only its 97 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 |
|---|---|---|
| 45. C3⋊(C9⋊C8) | Q8 | semidirect |
| 187. C3×C9 | #446 | semidirect |
| 262. C9 | #4828 | semidirect |
| 294. C3 | #10588510 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#6189 | 2 |
| C8×C3⋊Dic9 | 2 |
| C9×Dic3⋊C8 | 2 |
| C3×Dic9⋊C8 | 2 |
| #11720274 | 2 |
| #11720273 | 2 |
| #11720258 | 2 |
| #10590788 | 3 |
| #10588510 | 3 |