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. #11720525 | C2 | semidirect |
| 4. C3×#63368 | C2 | semidirect |
| 6. #11720268 | C2 | semidirect |
| 7. #11720264 | C2 | semidirect |
| 32. #63368 | D3 | semidirect |
| 196. C3×C9 | #485 | semidirect |
| 278. C9 | #4815 | semidirect |
| 315. C3 | #10588680 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C9×#892 | 2 |
| #11720960 | 2 |
| #11720525 | 2 |
| C3×#63368 | 2 |
| (C2×D3)⋊(C9⋊C8) | 2 |
| #11720268 | 2 |
| #11720264 | 2 |
| #10590521 | 3 |
| #10588680 | 3 |