Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
874 conjugacy classes of subgroups; only the 177 normal subgroups are shown.
This group has 874 conjugacy classes of subgroups — too many to draw. Only its 177 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 |
|---|---|---|
| 1. C2×#88635 | C2 | semidirect |
| 2. C2×#88525 | C2 | semidirect |
| 3. C2×C9×Dic12 | C2 | semidirect |
| 4. C2×C3×C8×D9 | C2 | semidirect |
| 5. C2×#88426 | C2 | semidirect |
| 6. #11720830 | C2 | direct (N × H) |
| 15. #88635 | C22 | semidirect |
| 17. #88525 | C22 | semidirect |
| 19. C9×Dic12 | C22 | semidirect |
| 20. C3×C8×D9 | C22 | semidirect |
| 21. #88426 | C22 | semidirect |
| 34. C2×C8×D9 | D3 | semidirect |
| 80. C8×D9 | C2×D3 | semidirect |
| 96. C2×Dic12 | D9 | semidirect |
| 139. C2×C3×C9 | #135 | semidirect |
| 166. Dic12 | C2×D9 | semidirect |
| 201. C3×C9 | C2×#135 | semidirect |
| 243. C2×C9 | #904 | semidirect |
| 286. C9 | C2×#904 | semidirect |
| 305. C2×C3 | #63481 | semidirect |
| 323. C3 | C2×#63481 | semidirect |
| 327. C2 | #11720830 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#88635 | 2 |
| C2×#88525 | 2 |
| C2×C9×Dic12 | 2 |
| C2×C3×C8×D9 | 2 |
| C2×#88426 | 2 |
| #11720830 | 2 |
| C2×#63808 | 3 |
| C2×#63481 | 3 |