Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
534 conjugacy classes of subgroups; only the 153 normal subgroups are shown.
This group has 534 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 |
|---|---|---|
| 2. C2×C9×#214 | C2 | semidirect |
| 3. C9×#869 | C2 | semidirect |
| 4. C4×C9×C3⋊C8 | C2 | semidirect |
| 30. C9×C3⋊C8 | D4 | semidirect |
| 32. #5076 | C9 | direct (N × H) |
| 53. C3×C4×C9 | SD16 | semidirect |
| 61. C2×#214 | C2×C9 | semidirect |
| 62. #869 | C2×C9 | semidirect |
| 64. C4×C3⋊C8 | C2×C9 | semidirect |
| 122. C4×C9 | #214 | semidirect |
| 128. C3×C9 | #492 | semidirect |
| 149. C3⋊C8 | D4×C9 | semidirect |
| 178. C3×C4 | C9×SD16 | semidirect |
| 185. C9 | #5076 | direct (N × H) |
| 207. C4 | C9×#214 | semidirect |
| 210. C3 | C9×#492 | 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×#214 | 2 |
| C9×#869 | 2 |
| C4×C9×C3⋊C8 | 2 |
| C3×#5076 | 3 |
| C9×#492 | 3 |