Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
330 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 330 conjugacy classes of subgroups — too many to draw. Only its 105 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×C8×C9 | Q8 | semidirect |
| 32. C3×C9⋊C8 | Q8 | semidirect |
| 83. C8×C9 | Dic6 | semidirect |
| 84. C9⋊C8 | Dic6 | semidirect |
| 125. C3×C9 | #498 | semidirect |
| 140. C3×C8 | Dic18 | semidirect |
| 174. C9 | #4680 | semidirect |
| 181. C8 | #6189 | semidirect |
| 195. C3 | #10588535 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11720969 | 2 |
| #11720540 | 2 |
| C9×#817 | 2 |
| C3×C8×Dic9 | 2 |
| #11720264 | 2 |
| #10590889 | 3 |
| #10588535 | 3 |