Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
530 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 530 conjugacy classes of subgroups — too many to draw. Only its 117 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×#874 | C2 | semidirect |
| 2. C3×#63436 | C2 | semidirect |
| 3. C2×#88421 | C2 | semidirect |
| 4. C4×C3⋊(C9⋊C8) | C2 | semidirect |
| 20. #63436 | D3 | semidirect |
| 31. C3⋊(C9⋊C8) | D4 | semidirect |
| 55. C3×C4×C9 | D8 | semidirect |
| 62. #874 | D9 | semidirect |
| 123. C4×C9 | #213 | semidirect |
| 129. C3×C9 | #493 | semidirect |
| 181. C3×C4 | #3673 | semidirect |
| 187. C9 | #5073 | semidirect |
| 212. C4 | #88421 | semidirect |
| 215. C3 | #10588755 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C9×#874 | 2 |
| C3×#63436 | 2 |
| C2×#88421 | 2 |
| C4×C3⋊(C9⋊C8) | 2 |
| #10590352 | 3 |
| #10588755 | 3 |