Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
428 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 428 conjugacy classes of subgroups — too many to draw. Only its 91 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 |
|---|---|---|
| 2. C9×#944 | C2 | semidirect |
| 5. C3×#63395 | C2 | semidirect |
| 6. #11720297 | C2 | semidirect |
| 7. Dic3⋊(C9⋊C8) | C2 | semidirect |
| 36. #63395 | D3 | semidirect |
| 95. C9×Dic3 | SD16 | semidirect |
| 98. #944 | D9 | semidirect |
| 223. C3×C9 | #461 | semidirect |
| 317. Dic3 | #3675 | semidirect |
| 320. C9 | #4818 | semidirect |
| 361. C3 | #10588768 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#88548 | 2 |
| C9×#944 | 2 |
| #11720993 | 2 |
| C2×#88426 | 2 |
| C3×#63395 | 2 |
| #11720297 | 2 |
| Dic3⋊(C9⋊C8) | 2 |
| #10591565 | 3 |
| #10588768 | 3 |