Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
620 conjugacy classes of subgroups; only the 135 normal subgroups are shown.
This group has 620 conjugacy classes of subgroups — too many to draw. Only its 135 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. #11721857 | C2 | semidirect |
| 2. C2×#88548 | C2 | semidirect |
| 4. #11721749 | C2 | semidirect |
| 5. C3×C9×#103 | C2 | semidirect |
| 6. #11720537 | C2 | semidirect |
| 7. #11720528 | C2 | semidirect |
| 34. C9×#103 | D3 | semidirect |
| 102. C3×#103 | D9 | semidirect |
| 203. #103 | C3⋊D9 | semidirect |
| 205. C3×C9 | #463 | semidirect |
| 288. C9 | #4819 | semidirect |
| 328. C3 | #10588499 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11721857 | 2 |
| C2×#88548 | 2 |
| C2×#88525 | 2 |
| #11721749 | 2 |
| C3×C9×#103 | 2 |
| #11720537 | 2 |
| #11720528 | 2 |
| #10592518 | 3 |
| #10588499 | 3 |