Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
364 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 364 conjugacy classes of subgroups — too many to draw. Only its 93 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. C9×C3⋊#95 | C2 | semidirect |
| 3. C9×#830 | C2 | semidirect |
| 7. C2×C3×D4×C9 | C4 | semidirect |
| 10. C3×C9×C4⋊C4 | C4 | semidirect |
| 34. #4537 | C9 | direct (N × H) |
| 45. C2×D4×C9 | Dic3 | semidirect |
| 51. C9×C4⋊C4 | Dic3 | semidirect |
| 71. C3⋊#95 | C2×C9 | semidirect |
| 72. #830 | C2×C9 | semidirect |
| 119. C2×C3×D4 | C4×C9 | semidirect |
| 128. C3×C4⋊C4 | C4×C9 | semidirect |
| 172. C3×C9 | #327 | semidirect |
| 227. C2×D4 | C9×Dic3 | semidirect |
| 231. C4⋊C4 | C9×Dic3 | semidirect |
| 270. C9 | #4537 | direct (N × H) |
| 315. C3 | C9×#327 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C9×#121 | 2 |
| C9×C3⋊#95 | 2 |
| C9×#830 | 2 |
| C3×#4537 | 3 |
| C9×#327 | 3 |