Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
520 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 520 conjugacy classes of subgroups — too many to draw. Only its 133 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. C3×C9×#137 | C2 | semidirect |
| 3. #11721865 | C2 | semidirect |
| 4. C2×#88548 | C2 | semidirect |
| 5. #11720581 | C2 | semidirect |
| 6. #11720557 | C2 | semidirect |
| 7. #11720555 | C2 | semidirect |
| 32. C9×#137 | D3 | semidirect |
| 95. C3×#137 | D9 | semidirect |
| 192. #137 | C3⋊D9 | semidirect |
| 199. C3×C9 | #471 | semidirect |
| 272. C9 | #5203 | semidirect |
| 305. C3 | #10588884 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C9×#137 | 2 |
| #11721867 | 2 |
| #11721865 | 2 |
| C2×#88548 | 2 |
| #11720581 | 2 |
| #11720557 | 2 |
| #11720555 | 2 |
| #10592902 | 3 |
| #10588884 | 3 |