Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
440 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 440 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. C2×#88548 | C2 | semidirect |
| 2. C9×#947 | C2 | semidirect |
| 3. #11720993 | C2 | semidirect |
| 5. C3×#63395 | C2 | semidirect |
| 6. #11720294 | C2 | semidirect |
| 7. Dic3⋊(C9⋊C8) | C2 | semidirect |
| 35. #63395 | D3 | semidirect |
| 100. #947 | D9 | semidirect |
| 230. C3×C9 | #463 | semidirect |
| 333. C9 | #4819 | semidirect |
| 378. C3 | #10588738 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#88548 | 2 |
| C9×#947 | 2 |
| #11720993 | 2 |
| C2×#88422 | 2 |
| C3×#63395 | 2 |
| #11720294 | 2 |
| Dic3⋊(C9⋊C8) | 2 |
| #10591568 | 3 |
| #10588738 | 3 |