Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
482 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 482 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. C3×#63512 | C2 | semidirect |
| 3. #11720951 | C2 | semidirect |
| 4. #11720882 | C2 | semidirect |
| 5. #11720585 | C2 | semidirect |
| 6. #11720300 | C2 | semidirect |
| 7. #11720299 | C2 | semidirect |
| 36. #63512 | D3 | semidirect |
| 115. #1010 | D9 | semidirect |
| 258. C3×C9 | #454 | semidirect |
| 370. C9 | #5201 | semidirect |
| 418. 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 |
| C3×#63512 | 2 |
| #11720951 | 2 |
| #11720882 | 2 |
| #11720585 | 2 |
| #11720300 | 2 |
| #11720299 | 2 |
| #10591684 | 3 |
| #10588926 | 3 |