Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
440 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 440 conjugacy classes of subgroups — too many to draw. Only its 83 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. C2×#88548 | C2 | semidirect |
| 2. C3×#63509 | C2 | semidirect |
| 3. #11720992 | C2 | semidirect |
| 5. C9×#835 | C2 | semidirect |
| 6. Dic9⋊(C3⋊C8) | C2 | semidirect |
| 7. #11720266 | C2 | semidirect |
| 30. #63509 | D3 | semidirect |
| 109. #835 | D9 | semidirect |
| 230. C3×C9 | #463 | semidirect |
| 333. C9 | #5057 | semidirect |
| 378. C3 | #10588499 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#88548 | 2 |
| C3×#63509 | 2 |
| #11720992 | 2 |
| C2×#88417 | 2 |
| C9×#835 | 2 |
| Dic9⋊(C3⋊C8) | 2 |
| #11720266 | 2 |
| #10591568 | 3 |
| #10588499 | 3 |