Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
650 conjugacy classes of subgroups; only the 153 normal subgroups are shown.
This group has 650 conjugacy classes of subgroups — too many to draw. Only its 153 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. C2×#88525 | C2 | semidirect |
| 2. C2×#88523 | C2 | semidirect |
| 3. #11721751 | C2 | semidirect |
| 4. C3×C9×#106 | C2 | semidirect |
| 5. #11720528 | C2 | semidirect |
| 25. C9×#106 | D3 | semidirect |
| 37. C3×C8×C9 | D4 | semidirect |
| 75. C3×#106 | D9 | semidirect |
| 101. C8×C9 | D12 | semidirect |
| 149. #106 | C3⋊D9 | semidirect |
| 151. C3×C9 | #469 | semidirect |
| 172. C3×C8 | D36 | semidirect |
| 214. C9 | #4865 | semidirect |
| 226. C8 | C4⋊(C3⋊D9) | semidirect |
| 245. C3 | #10588545 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#88525 | 2 |
| C2×#88523 | 2 |
| #11721751 | 2 |
| C3×C9×#106 | 2 |
| #11720528 | 2 |
| #10592564 | 3 |
| #10588545 | 3 |