Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
760 conjugacy classes of subgroups; only the 129 normal subgroups are shown.
This group has 760 conjugacy classes of subgroups — too many to draw. Only its 129 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. C3×C9×H(5,𝔽2) | C2 | semidirect |
| 2. C9×#937 | C2 | semidirect |
| 3. C9×#834 | C2 | semidirect |
| 6. C23×D3×C9 | C22 | semidirect |
| 11. C9×#217 | C22 | semidirect |
| 16. C9×H(5,𝔽2) | D3 | semidirect |
| 21. C23×C3×C9 | D4 | semidirect |
| 29. C2×C3×C4×C9 | D4 | semidirect |
| 33. #5244 | C9 | direct (N × H) |
| 62. C3×H(5,𝔽2) | C2×C9 | semidirect |
| 65. #937 | C2×C9 | semidirect |
| 67. #834 | C2×C9 | semidirect |
| 86. C23×C9 | #67 | semidirect |
| 99. C2×C4×C9 | #67 | semidirect |
| 106. C23×D3 | C22×C9 | semidirect |
| 120. #217 | C22×C9 | semidirect |
| 148. H(5,𝔽2) | D3×C9 | semidirect |
| 151. C3×C9 | B(4,𝔽2) | semidirect |
| 159. C23×C3 | D4×C9 | semidirect |
| 180. C2×C3×C4 | D4×C9 | semidirect |
| 230. C9 | #5244 | direct (N × H) |
| 234. C23 | C9×#67 | semidirect |
| 242. C2×C4 | C9×#67 | semidirect |
| 265. 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 |
|---|---|
| C3×C9×H(5,𝔽2) | 2 |
| C9×#937 | 2 |
| C9×#834 | 2 |
| C3×#5244 | 3 |
| C9×B(4,𝔽2) | 3 |