Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
372 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 372 conjugacy classes of subgroups — too many to draw. Only its 83 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. #11721866 | C2 | semidirect |
| 3. C9×#948 | C2 | semidirect |
| 4. C2×#88415 | C2 | semidirect |
| 5. #11720290 | C2 | semidirect |
| 6. #11720287 | C2 | semidirect |
| 7. #11720280 | C2 | semidirect |
| 107. #948 | D9 | semidirect |
| 226. C3×C9 | #471 | semidirect |
| 318. C9 | #5200 | semidirect |
| 355. C3 | #10588822 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11721866 | 2 |
| C3×#63512 | 2 |
| C9×#948 | 2 |
| C2×#88415 | 2 |
| #11720290 | 2 |
| #11720287 | 2 |
| #11720280 | 2 |
| #10591679 | 3 |
| #10588822 | 3 |