Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
540 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 540 conjugacy classes of subgroups — too many to draw. Only its 115 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. #11721833 | C2 | semidirect |
| 2. C2×#88544 | C2 | semidirect |
| 3. #11721783 | C2 | semidirect |
| 4. #11721782 | C2 | semidirect |
| 5. C3×C9×#100 | C2 | semidirect |
| 6. #11720557 | C2 | semidirect |
| 7. #11720555 | C2 | semidirect |
| 36. C9×#100 | D3 | semidirect |
| 104. C3×#100 | D9 | semidirect |
| 202. #100 | C3⋊D9 | semidirect |
| 203. C3×C9 | #472 | semidirect |
| 280. C9 | #4749 | semidirect |
| 316. C3 | #10588429 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11721833 | 2 |
| C2×#88544 | 2 |
| #11721783 | 2 |
| #11721782 | 2 |
| C3×C9×#100 | 2 |
| #11720557 | 2 |
| #11720555 | 2 |
| #10592448 | 3 |
| #10588429 | 3 |