Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
594 conjugacy classes of subgroups; only the 153 normal subgroups are shown.
This group has 594 conjugacy classes of subgroups — too many to draw. Only its 153 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×#127 | C2 | semidirect |
| 2. C2×C9×#213 | C2 | semidirect |
| 3. C9×#874 | C2 | semidirect |
| 4. C4×C9×C3⋊C8 | C2 | semidirect |
| 21. C9×#127 | D3 | semidirect |
| 31. C9×C3⋊C8 | D4 | semidirect |
| 33. #5073 | C9 | direct (N × H) |
| 56. C3×C4×C9 | D8 | semidirect |
| 61. C3×#127 | C2×C9 | semidirect |
| 63. C2×#213 | C2×C9 | semidirect |
| 64. #874 | C2×C9 | semidirect |
| 66. C4×C3⋊C8 | C2×C9 | semidirect |
| 129. C4×C9 | #213 | semidirect |
| 133. #127 | D3×C9 | semidirect |
| 135. C3×C9 | #493 | semidirect |
| 158. C3⋊C8 | D4×C9 | semidirect |
| 192. C3×C4 | C9×D8 | semidirect |
| 198. C9 | #5073 | direct (N × H) |
| 224. C4 | C9×#213 | semidirect |
| 227. C3 | C9×#493 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C9×#127 | 2 |
| C2×C9×#213 | 2 |
| C9×#874 | 2 |
| C4×C9×C3⋊C8 | 2 |
| C3×#5073 | 3 |
| C9×#493 | 3 |