Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
396 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 396 conjugacy classes of subgroups — too many to draw. Only its 85 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×#897 | C2 | semidirect |
| 3. C2×#88425 | C2 | semidirect |
| 4. C2×#88420 | C2 | semidirect |
| 5. #11720525 | C2 | semidirect |
| 6. C3×#63369 | C2 | semidirect |
| 7. #11720298 | C2 | semidirect |
| 35. #63369 | D3 | semidirect |
| 52. C3⋊(C9⋊C8) | D4 | semidirect |
| 105. #897 | D9 | semidirect |
| 222. C3×C9 | #468 | semidirect |
| 318. C9 | #4780 | semidirect |
| 362. C3 | #10588732 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C9×#897 | 2 |
| #11721037 | 2 |
| C2×#88425 | 2 |
| C2×#88420 | 2 |
| #11720525 | 2 |
| C3×#63369 | 2 |
| #11720298 | 2 |
| #10590503 | 3 |
| #10588732 | 3 |