Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
614 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 614 conjugacy classes of subgroups — too many to draw. Only its 113 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. C3×#63486 | C2 | semidirect |
| 3. C2×#88423 | C2 | semidirect |
| 4. #11720571 | C2 | semidirect |
| 5. #11720294 | C2 | semidirect |
| 13. C2×C3×Dic18 | C22 | semidirect |
| 14. C2×C3⋊(C9⋊C8) | C22 | semidirect |
| 16. C3×C4⋊Dic9 | C22 | semidirect |
| 26. #63486 | D3 | semidirect |
| 64. C2×Dic18 | C2×D3 | semidirect |
| 67. C4⋊Dic9 | C2×D3 | semidirect |
| 73. C22×C3×C9 | SD16 | semidirect |
| 181. C22×C9 | #215 | semidirect |
| 194. C3×C9 | #450 | semidirect |
| 267. C22×C3 | #3672 | semidirect |
| 287. C9 | #5046 | semidirect |
| 323. C22 | #88423 | semidirect |
| 330. C3 | #10588897 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C9×D12 | 2 |
| C3×#63486 | 2 |
| C2×#88423 | 2 |
| #11720571 | 2 |
| #11720294 | 2 |
| #10591169 | 3 |
| #10588897 | 3 |