Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
404 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 404 conjugacy classes of subgroups — too many to draw. Only its 95 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. Q8×C9×Dic3 | C2 | semidirect |
| 3. C2×C3×#3674 | C2 | semidirect |
| 5. #11720268 | C2 | semidirect |
| 7. Dic3⋊(C9⋊C8) | C2 | semidirect |
| 33. C2×#3674 | D3 | semidirect |
| 99. Q8×Dic3 | D9 | semidirect |
| 220. C3×C9 | #464 | semidirect |
| 315. C9 | #5185 | semidirect |
| 355. C3 | #10588711 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#88548 | 2 |
| Q8×C9×Dic3 | 2 |
| C2×C3×#3674 | 2 |
| #11720952 | 2 |
| #11720268 | 2 |
| #11720267 | 2 |
| Dic3⋊(C9⋊C8) | 2 |
| #10591607 | 3 |
| #10588711 | 3 |