Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
434 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 434 conjugacy classes of subgroups — too many to draw. Only its 91 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. C2×C9×#214 | C2 | semidirect |
| 3. Dic6×Dic9 | C2 | semidirect |
| 4. C2×#88425 | C2 | semidirect |
| 5. #11720576 | C2 | semidirect |
| 6. #11720283 | C2 | semidirect |
| 7. Dic9⋊(C3⋊C8) | C2 | semidirect |
| 52. C9×Dic6 | D4 | semidirect |
| 98. C3×Dic9 | SD16 | semidirect |
| 105. C2×#214 | D9 | semidirect |
| 221. Dic9 | #214 | semidirect |
| 229. C3×C9 | #460 | semidirect |
| 264. Dic6 | #611 | semidirect |
| 332. C9 | #5075 | semidirect |
| 378. C3 | #10588843 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#63502 | 2 |
| C2×C9×#214 | 2 |
| Dic6×Dic9 | 2 |
| C2×#88425 | 2 |
| #11720576 | 2 |
| #11720283 | 2 |
| Dic9⋊(C3⋊C8) | 2 |
| #10591438 | 3 |
| #10588843 | 3 |