Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
360 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 360 conjugacy classes of subgroups — too many to draw. Only its 71 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. C2×C3×#3674 | C2 | semidirect |
| 5. C9×#836 | C2 | semidirect |
| 6. #11720289 | C2 | semidirect |
| 7. #11720285 | C2 | semidirect |
| 34. C2×#3674 | D3 | semidirect |
| 111. #836 | D9 | semidirect |
| 222. C3×C9 | #473 | semidirect |
| 310. C9 | #5192 | semidirect |
| 344. C3 | #10588435 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11721853 | 2 |
| C2×C3×#3674 | 2 |
| #11720871 | 2 |
| #11720861 | 2 |
| C9×#836 | 2 |
| #11720289 | 2 |
| #11720285 | 2 |
| #10591543 | 3 |
| #10588435 | 3 |