Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
374 conjugacy classes of subgroups; only the 69 normal subgroups are shown.
This group has 374 conjugacy classes of subgroups — too many to draw. Only its 69 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. #11721782 | C2 | semidirect |
| 2. #11720895 | C2 | semidirect |
| 3. C2×#88425 | C2 | semidirect |
| 5. C9×#824 | C2 | semidirect |
| 6. C3×#63383 | C2 | semidirect |
| 7. #11720286 | C2 | semidirect |
| 38. #63383 | D3 | semidirect |
| 112. #824 | D9 | semidirect |
| 224. C3×C9 | #471 | semidirect |
| 314. C9 | #4748 | semidirect |
| 351. C3 | #10588434 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11721782 | 2 |
| #11720895 | 2 |
| C2×#88425 | 2 |
| #11720868 | 2 |
| C9×#824 | 2 |
| C3×#63383 | 2 |
| #11720286 | 2 |
| #10590991 | 3 |
| #10588434 | 3 |