Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
440 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 440 conjugacy classes of subgroups — too many to draw. Only its 89 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×#944 | C2 | semidirect |
| 3. C2×C3×#3674 | C2 | semidirect |
| 5. C2×#88427 | C2 | semidirect |
| 7. #11720258 | C2 | semidirect |
| 35. C2×#3674 | D3 | semidirect |
| 98. #944 | D9 | semidirect |
| 215. C3×C9 | #497 | semidirect |
| 304. C9 | #5190 | semidirect |
| 340. C3 | #10588771 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#88548 | 2 |
| C9×#944 | 2 |
| C2×C3×#3674 | 2 |
| #11720952 | 2 |
| C2×#88427 | 2 |
| C2×#88426 | 2 |
| #11720258 | 2 |
| #10591608 | 3 |
| #10588771 | 3 |