Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
412 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 412 conjugacy classes of subgroups — too many to draw. Only its 89 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 |
|---|---|---|
| 2. C9×#926 | C2 | semidirect |
| 3. C3×#63389 | C2 | semidirect |
| 4. #11720267 | C2 | semidirect |
| 5. #11720267 | C2 | semidirect |
| 6. #11720264 | C2 | semidirect |
| 7. #11720262 | C2 | semidirect |
| 31. #63389 | D3 | semidirect |
| 96. #926 | D9 | semidirect |
| 222. C3×C9 | #482 | semidirect |
| 326. C9 | #4737 | semidirect |
| 370. C3 | #10588684 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11721819 | 2 |
| C9×#926 | 2 |
| C3×#63389 | 2 |
| #11720267 | 2 |
| #11720264 | 2 |
| #11720262 | 2 |
| #10591136 | 3 |
| #10588684 | 3 |