Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
730 conjugacy classes of subgroups; only the 135 normal subgroups are shown.
This group has 730 conjugacy classes of subgroups — too many to draw. Only its 135 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 |
|---|---|---|
| 1. #11722667 | C2 | semidirect |
| 2. C3×C9×#124 | C2 | semidirect |
| 3. #11721833 | C2 | semidirect |
| 4. #11720581 | C2 | semidirect |
| 5. #11720518 | C2 | semidirect |
| 25. C9×#124 | D3 | semidirect |
| 77. C3×#124 | D9 | semidirect |
| 158. #124 | C3⋊D9 | semidirect |
| 161. C3×C9 | #454 | semidirect |
| 226. C9 | #5062 | semidirect |
| 257. C3 | #10588742 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11722667 | 2 |
| C3×C9×#124 | 2 |
| #11721833 | 2 |
| #11720581 | 2 |
| #11720518 | 2 |
| #10592761 | 3 |
| #10588742 | 3 |