Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
332 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 332 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 |
|---|---|---|
| 2. C8×C3⋊Dic9 | C2 | semidirect |
| 4. C3×Dic9⋊C8 | C2 | semidirect |
| 6. #11720275 | C2 | semidirect |
| 7. Dic9⋊(C3⋊C8) | C2 | semidirect |
| 33. Dic9⋊C8 | D3 | semidirect |
| 197. C3×C9 | #433 | semidirect |
| 280. C9 | #4840 | semidirect |
| 317. C3 | #10588400 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11720959 | 2 |
| C8×C3⋊Dic9 | 2 |
| C9×(C2×D3)⋊C8 | 2 |
| C3×Dic9⋊C8 | 2 |
| (C2×D3)⋊(C9⋊C8) | 2 |
| #11720275 | 2 |
| Dic9⋊(C3⋊C8) | 2 |
| #10590698 | 3 |
| #10588400 | 3 |