Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
298 conjugacy classes of subgroups; only the 65 normal subgroups are shown.
This group has 298 conjugacy classes of subgroups — too many to draw. Only its 65 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. C9×#912 | C2 | semidirect |
| 2. D3×D72 | C2 | semidirect |
| 3. #11720563 | C2 | semidirect |
| 4. C3×#63385 | C2 | semidirect |
| 5. #11720243 | C2 | semidirect |
| 6. #11720242 | C2 | semidirect |
| 7. #11720237 | C2 | semidirect |
| 12. C3×C9×D8 | C22 | semidirect |
| 15. C9×Dic12 | C22 | semidirect |
| 19. C3⋊(C9⋊C16) | C22 | semidirect |
| 20. C3×C9⋊C16 | C22 | semidirect |
| 34. #63385 | D3 | semidirect |
| 65. C9×D8 | C2×D3 | semidirect |
| 73. C9⋊C16 | C2×D3 | semidirect |
| 83. #912 | D9 | semidirect |
| 136. C3×D8 | C2×D9 | semidirect |
| 141. Dic12 | C2×D9 | semidirect |
| 179. C3×C9 | #509 | semidirect |
| 225. D8 | D3×D9 | semidirect |
| 250. C9 | #4911 | semidirect |
| 284. C3 | #10588873 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C9×#912 | 2 |
| D3×D72 | 2 |
| #11720563 | 2 |
| C3×#63385 | 2 |
| #11720243 | 2 |
| #11720242 | 2 |
| #11720237 | 2 |
| #10591024 | 3 |
| #10588873 | 3 |