Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
338 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 338 conjugacy classes of subgroups — too many to draw. Only its 93 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. C9×#815 | C2 | semidirect |
| 4. C3×Dic9⋊C8 | C2 | semidirect |
| 6. Dic9⋊(C3⋊C8) | C2 | semidirect |
| 7. Dic3×C9⋊C8 | C2 | semidirect |
| 34. Dic9⋊C8 | D3 | semidirect |
| 96. #815 | D9 | semidirect |
| 201. C3×C9 | #433 | semidirect |
| 289. C9 | #4840 | semidirect |
| 327. C3 | #10588390 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11720931 | 2 |
| #11720542 | 2 |
| C9×#815 | 2 |
| C3×Dic9⋊C8 | 2 |
| #11720282 | 2 |
| Dic9⋊(C3⋊C8) | 2 |
| Dic3×C9⋊C8 | 2 |
| #10590647 | 3 |
| #10588390 | 3 |