Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
484 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 484 conjugacy classes of subgroups — too many to draw. Only its 85 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. #11721838 | C2 | semidirect |
| 2. C2×C9×#213 | C2 | semidirect |
| 3. #11721045 | C2 | semidirect |
| 4. C2×#88414 | C2 | semidirect |
| 5. C3×#63392 | C2 | semidirect |
| 6. #11720295 | C2 | semidirect |
| 7. #11720278 | C2 | semidirect |
| 36. #63392 | D3 | semidirect |
| 53. C9×C3⋊C8 | D4 | semidirect |
| 108. C2×#213 | D9 | semidirect |
| 248. C3×C9 | #469 | semidirect |
| 292. C3⋊C8 | #611 | semidirect |
| 366. C9 | #4782 | semidirect |
| 417. C3 | #10588839 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11721838 | 2 |
| C2×C9×#213 | 2 |
| #11721045 | 2 |
| C2×#88414 | 2 |
| C3×#63392 | 2 |
| #11720295 | 2 |
| #11720278 | 2 |
| #10591454 | 3 |
| #10588839 | 3 |