Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
338 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 338 conjugacy classes of subgroups — too many to draw. Only its 117 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. C3⋊(C9⋊C8) | Q8 | semidirect |
| 129. C3×C9 | #498 | semidirect |
| 185. C9 | #5080 | semidirect |
| 210. C3 | #10588760 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C9×#869 | 2 |
| C3×#63431 | 2 |
| C4×C3⋊(C9⋊C8) | 2 |
| #11720265 | 2 |
| #10590309 | 3 |
| #10588760 | 3 |