Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
466 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 466 conjugacy classes of subgroups — too many to draw. Only its 133 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 |
|---|---|---|
| 4. C9×#815 | C2 | semidirect |
| 5. C3×#63375 | C2 | semidirect |
| 6. C3⋊C8×Dic9 | C2 | semidirect |
| 7. Dic3×C9⋊C8 | C2 | semidirect |
| 13. C8×C3⋊D9 | C4 | semidirect |
| 20. #88414 | C4 | semidirect |
| 33. #63375 | D3 | semidirect |
| 93. #815 | D9 | semidirect |
| 186. C3×C9 | #405 | semidirect |
| 260. C9 | #4708 | semidirect |
| 290. C3 | #10588389 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C8×C3⋊D9 | 2 |
| #11720931 | 2 |
| C2×#88414 | 2 |
| C9×#815 | 2 |
| C3×#63375 | 2 |
| C3⋊C8×Dic9 | 2 |
| Dic3×C9⋊C8 | 2 |
| #10590703 | 3 |
| #10588389 | 3 |