Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
720 conjugacy classes of subgroups; only the 155 normal subgroups are shown.
This group has 720 conjugacy classes of subgroups — too many to draw. Only its 155 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×#124 | C2 | semidirect |
| 2. C2×#88548 | C2 | semidirect |
| 3. C2×#88544 | C2 | semidirect |
| 4. #11721711 | C2 | semidirect |
| 5. #11720516 | C2 | semidirect |
| 22. C9×#124 | D3 | semidirect |
| 37. C3⋊(C9⋊C8) | D4 | semidirect |
| 66. C3×#124 | D9 | semidirect |
| 140. #124 | C3⋊D9 | semidirect |
| 142. C3×C9 | #496 | semidirect |
| 199. C9 | #5058 | semidirect |
| 227. C3 | #10588739 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C9×#124 | 2 |
| C2×#88548 | 2 |
| C2×#88544 | 2 |
| #11721711 | 2 |
| #11720516 | 2 |
| #10592757 | 3 |
| #10588739 | 3 |