Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
472 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 472 conjugacy classes of subgroups — too many to draw. Only its 93 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×#63437 | C2 | semidirect |
| 3. C2×#88423 | C2 | semidirect |
| 4. C2×#88421 | C2 | semidirect |
| 5. #11720516 | C2 | semidirect |
| 25. #63437 | D3 | semidirect |
| 38. C3⋊(C9⋊C8) | D4 | semidirect |
| 76. #874 | D9 | semidirect |
| 154. C3×C9 | #496 | semidirect |
| 220. C9 | #5058 | semidirect |
| 251. C3 | #10588756 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C9×#874 | 2 |
| C3×#63437 | 2 |
| C2×#88423 | 2 |
| C2×#88421 | 2 |
| #11720516 | 2 |
| #10590354 | 3 |
| #10588756 | 3 |