Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
404 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 404 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. #11720913 | C2 | semidirect |
| 4. C2×#88418 | C2 | semidirect |
| 6. Dic9⋊(C3⋊C8) | C2 | semidirect |
| 7. #11720268 | C2 | semidirect |
| 220. C3×C9 | #464 | semidirect |
| 315. C9 | #5054 | semidirect |
| 355. C3 | #10588447 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#88543 | 2 |
| C3×#63498 | 2 |
| #11720913 | 2 |
| C2×#88418 | 2 |
| C9×#832 | 2 |
| Dic9⋊(C3⋊C8) | 2 |
| #11720268 | 2 |
| #10591441 | 3 |
| #10588447 | 3 |