Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
508 conjugacy classes of subgroups; only the 129 normal subgroups are shown.
This group has 508 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×#124 | C2 | semidirect |
| 2. C2×C9×#215 | C2 | semidirect |
| 3. C2×C9×#213 | C2 | semidirect |
| 4. C9×#874 | C2 | semidirect |
| 5. C9×#803 | C2 | semidirect |
| 26. C9×#124 | D3 | semidirect |
| 38. C9×C3⋊C8 | D4 | semidirect |
| 40. #5058 | C9 | direct (N × H) |
| 75. C3×#124 | C2×C9 | semidirect |
| 77. C2×#215 | C2×C9 | semidirect |
| 78. C2×#213 | C2×C9 | semidirect |
| 79. #874 | C2×C9 | semidirect |
| 81. #803 | C2×C9 | semidirect |
| 162. #124 | D3×C9 | semidirect |
| 164. C3×C9 | #496 | semidirect |
| 192. C3⋊C8 | D4×C9 | semidirect |
| 237. C9 | #5058 | direct (N × H) |
| 269. C3 | C9×#496 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C9×#124 | 2 |
| C2×C9×#215 | 2 |
| C2×C9×#213 | 2 |
| C9×#874 | 2 |
| C9×#803 | 2 |
| C3×#5058 | 3 |
| C9×#496 | 3 |