Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
480 conjugacy classes of subgroups; only the 159 normal subgroups are shown.
This group has 480 conjugacy classes of subgroups — too many to draw. Only its 159 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 |
|---|---|---|
| 2. C3×C9×#97 | C2 | semidirect |
| 4. #11720537 | C2 | semidirect |
| 5. C4×C3⋊(C9⋊C8) | C2 | semidirect |
| 21. C9×#97 | D3 | semidirect |
| 58. C3×#97 | D9 | semidirect |
| 117. #97 | C3⋊D9 | semidirect |
| 119. C3×C9 | #433 | semidirect |
| 164. C9 | #4709 | semidirect |
| 186. C3 | #10588390 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11721709 | 2 |
| C3×C9×#97 | 2 |
| #11720542 | 2 |
| #11720537 | 2 |
| C4×C3⋊(C9⋊C8) | 2 |
| #10592408 | 3 |
| #10588390 | 3 |