Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
350 conjugacy classes of subgroups; only the 73 normal subgroups are shown.
This group has 350 conjugacy classes of subgroups — too many to draw. Only its 73 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. C3×#63469 | C2 | semidirect |
| 2. C2×#88424 | C2 | semidirect |
| 4. #11720869 | C2 | semidirect |
| 5. #11720556 | C2 | semidirect |
| 6. C9×#823 | C2 | semidirect |
| 7. #11720285 | C2 | semidirect |
| 35. #63469 | D3 | semidirect |
| 111. #823 | D9 | semidirect |
| 217. C3×C9 | #471 | semidirect |
| 303. C9 | #5141 | semidirect |
| 339. C3 | #10588428 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#63469 | 2 |
| C2×#88424 | 2 |
| #11720883 | 2 |
| #11720869 | 2 |
| #11720556 | 2 |
| C9×#823 | 2 |
| #11720285 | 2 |
| #10590996 | 3 |
| #10588428 | 3 |