Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
506 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 506 conjugacy classes of subgroups — too many to draw. Only its 89 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. C9×#1010 | C2 | semidirect |
| 2. #11721867 | C2 | semidirect |
| 3. #11720953 | C2 | semidirect |
| 4. #11720885 | C2 | semidirect |
| 5. C3×#63396 | C2 | semidirect |
| 6. #11720301 | C2 | semidirect |
| 7. #11720299 | C2 | semidirect |
| 40. #63396 | D3 | semidirect |
| 117. #1010 | D9 | semidirect |
| 265. C3×C9 | #454 | semidirect |
| 381. C9 | #4827 | semidirect |
| 430. C3 | #10588926 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C9×#1010 | 2 |
| #11721867 | 2 |
| #11720953 | 2 |
| #11720885 | 2 |
| C3×#63396 | 2 |
| #11720301 | 2 |
| #11720299 | 2 |
| #10591685 | 3 |
| #10588926 | 3 |