Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
370 conjugacy classes of subgroups; only the 77 normal subgroups are shown.
This group has 370 conjugacy classes of subgroups — too many to draw. Only its 77 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. C9×#907 | C2 | semidirect |
| 2. #11720885 | C2 | semidirect |
| 3. #11720882 | C2 | semidirect |
| 4. C2×#88417 | C2 | semidirect |
| 5. #11720557 | C2 | semidirect |
| 6. C3×#63383 | C2 | semidirect |
| 7. #11720280 | C2 | semidirect |
| 38. #63383 | D3 | semidirect |
| 106. #907 | D9 | semidirect |
| 222. C3×C9 | #472 | semidirect |
| 314. C9 | #4749 | semidirect |
| 354. C3 | #10588823 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C9×#907 | 2 |
| #11720885 | 2 |
| #11720882 | 2 |
| C2×#88417 | 2 |
| #11720557 | 2 |
| C3×#63383 | 2 |
| #11720280 | 2 |
| #10590997 | 3 |
| #10588823 | 3 |