Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
324 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 324 conjugacy classes of subgroups — too many to draw. Only its 83 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 |
|---|---|---|
| 3. #11720526 | C2 | semidirect |
| 4. C3×#63366 | C2 | semidirect |
| 5. #11720298 | C2 | semidirect |
| 6. #11720297 | C2 | semidirect |
| 35. #63366 | D3 | semidirect |
| 196. C3×C9 | #485 | semidirect |
| 278. C9 | #4888 | semidirect |
| 315. C3 | #10588725 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C9×#897 | 2 |
| #11720906 | 2 |
| #11720526 | 2 |
| C3×#63366 | 2 |
| #11720298 | 2 |
| #11720297 | 2 |
| (C2×D3)⋊(C9⋊C8) | 2 |
| #10590448 | 3 |
| #10588725 | 3 |