Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
380 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 380 conjugacy classes of subgroups — too many to draw. Only its 71 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. C2×#88543 | C2 | semidirect |
| 3. #11720869 | C2 | semidirect |
| 4. #11720859 | C2 | semidirect |
| 5. C9×#833 | C2 | semidirect |
| 6. #11720290 | C2 | semidirect |
| 7. #11720286 | C2 | semidirect |
| 111. #833 | D9 | semidirect |
| 226. C3×C9 | #471 | semidirect |
| 318. C9 | #5200 | semidirect |
| 355. C3 | #10588428 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#88543 | 2 |
| C3×#63495 | 2 |
| #11720869 | 2 |
| #11720859 | 2 |
| C9×#833 | 2 |
| #11720290 | 2 |
| #11720286 | 2 |
| #10591507 | 3 |
| #10588428 | 3 |