Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
516 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 516 conjugacy classes of subgroups — too many to draw. Only its 109 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. C2×C3×C8×D9 | C2 | semidirect |
| 3. #11720907 | C2 | semidirect |
| 4. #11720539 | C2 | semidirect |
| 5. C9×#821 | C2 | semidirect |
| 6. #11720295 | C2 | semidirect |
| 7. #11720269 | C2 | semidirect |
| 16. #88638 | C4 | semidirect |
| 32. C2×C8×D9 | D3 | semidirect |
| 111. #821 | D9 | semidirect |
| 232. C3×C9 | #416 | semidirect |
| 333. C9 | #5113 | semidirect |
| 378. C3 | #10588452 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#88638 | 2 |
| C2×C3×C8×D9 | 2 |
| #11720907 | 2 |
| #11720539 | 2 |
| C9×#821 | 2 |
| #11720295 | 2 |
| #11720269 | 2 |
| #10590954 | 3 |
| #10588452 | 3 |