Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
470 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 470 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 |
|---|---|---|
| 2. C9×#951 | C2 | semidirect |
| 3. #11720930 | C2 | semidirect |
| 4. #11720893 | C2 | semidirect |
| 5. #11720585 | C2 | semidirect |
| 6. #11720291 | C2 | semidirect |
| 7. #11720289 | C2 | semidirect |
| 117. #951 | D9 | semidirect |
| 254. C3×C9 | #456 | semidirect |
| 362. C9 | #5246 | semidirect |
| 407. C3 | #10588885 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#63716 | 2 |
| C9×#951 | 2 |
| #11720930 | 2 |
| #11720893 | 2 |
| #11720585 | 2 |
| #11720291 | 2 |
| #11720289 | 2 |
| #10591687 | 3 |
| #10588885 | 3 |