Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
257 conjugacy classes of subgroups; only the 63 normal subgroups are shown.
This group has 257 conjugacy classes of subgroups — too many to draw. Only its 63 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. #11722559 | C2 | semidirect |
| 2. #11721339 | C2 | semidirect |
| 4. C9×#578 | C3 | semidirect |
| 5. #578⋊C9 | C3 | semidirect |
| 11. C9×2−1+4 | C2×C3 | semidirect |
| 12. 2−1+4⋊C9 | C2×C3 | semidirect |
| 16. C9×#131 | C2×C3 | semidirect |
| 17. #131⋊C9 | C2×C3 | semidirect |
| 66. #578 | 3−1+2 | semidirect |
| 92. 2−1+4 | C2×3−1+2 | semidirect |
| 96. #131 | C2×3−1+2 | semidirect |
| 139. C9 | #578⋊C3 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11722559 | 2 |
| #11721339 | 2 |
| C3×#578⋊C3 | 3 |
| C9×#578 | 3 |
| #578⋊C9 | 3 |
| D8×3−1+2 | 4 |