Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
646 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 646 conjugacy classes of subgroups — too many to draw. Only its 117 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×#1004 | C2 | semidirect |
| 2. C9×#937 | C2 | semidirect |
| 3. C9×#882 | C2 | semidirect |
| 4. C3×C9×#99 | C2 | semidirect |
| 5. C9×#806 | C2 | semidirect |
| 8. C23×D3×C9 | C22 | semidirect |
| 17. C3×C9×C22⋊C4 | C22 | semidirect |
| 18. C9×#217 | C22 | semidirect |
| 31. C9×#99 | D3 | semidirect |
| 32. C23×C3×C9 | D4 | semidirect |
| 38. C22×D3×C9 | D4 | semidirect |
| 41. C2×C3×C4×C9 | D4 | semidirect |
| 48. C2×C9×Dic3 | D4 | semidirect |
| 54. #4741 | C9 | direct (N × H) |
| 82. C9×C22⋊C4 | C2×D3 | semidirect |
| 101. #1004 | C2×C9 | semidirect |
| 104. #937 | C2×C9 | semidirect |
| 105. #882 | C2×C9 | semidirect |
| 108. C3×#99 | C2×C9 | semidirect |
| 110. #806 | C2×C9 | semidirect |
| 139. C23×C9 | D12 | semidirect |
| 157. C2×C4×C9 | D12 | semidirect |
| 166. C23×D3 | C22×C9 | semidirect |
| 188. C3×C22⋊C4 | C22×C9 | semidirect |
| 190. #217 | C22×C9 | semidirect |
| 238. #99 | D3×C9 | semidirect |
| 239. C3×C9 | B(4,𝔽2) | semidirect |
| 247. C23×C3 | D4×C9 | semidirect |
| 255. C22×D3 | D4×C9 | semidirect |
| 274. C2×C3×C4 | D4×C9 | semidirect |
| 282. C2×Dic3 | D4×C9 | semidirect |
| 315. C22⋊C4 | C2×D3×C9 | semidirect |
| 359. C9 | #4741 | direct (N × H) |
| 365. C23 | C9×D12 | semidirect |
| 380. C2×C4 | C9×D12 | semidirect |
| 415. C3 | C9×B(4,𝔽2) | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C9×#1004 | 2 |
| C9×#937 | 2 |
| C9×#882 | 2 |
| C3×C9×#99 | 2 |
| C9×#806 | 2 |
| C3×#4741 | 3 |
| C9×B(4,𝔽2) | 3 |