Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
810 conjugacy classes of subgroups; only the 195 normal subgroups are shown.
This group has 810 conjugacy classes of subgroups — too many to draw. Only its 195 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. C3×C9×#127 | C2 | semidirect |
| 2. C2×#88544 | C2 | semidirect |
| 3. #11721711 | C2 | semidirect |
| 4. C4×C3⋊(C9⋊C8) | C2 | semidirect |
| 18. C9×#127 | D3 | semidirect |
| 30. C3⋊(C9⋊C8) | D4 | semidirect |
| 52. C3×C4×C9 | D8 | semidirect |
| 54. C3×#127 | D9 | semidirect |
| 111. C4×C9 | #213 | semidirect |
| 115. #127 | C3⋊D9 | semidirect |
| 117. C3×C9 | #493 | semidirect |
| 161. C3×C4 | #3673 | semidirect |
| 166. C9 | #5073 | semidirect |
| 189. C4 | #88544 | semidirect |
| 191. C3 | #10588755 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C9×#127 | 2 |
| C2×#88544 | 2 |
| #11721711 | 2 |
| C4×C3⋊(C9⋊C8) | 2 |
| #10592772 | 3 |
| #10588755 | 3 |