Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
472 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 472 conjugacy classes of subgroups — too many to draw. Only its 141 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. C2×C9×D24 | C2 | semidirect |
| 2. C2×C9×#204 | C2 | semidirect |
| 3. C9×#875 | C2 | semidirect |
| 4. C9×#874 | C2 | semidirect |
| 5. C3×C9×#97 | C2 | semidirect |
| 27. C9×#97 | D3 | semidirect |
| 38. C3×C8×C9 | D4 | semidirect |
| 40. #4712 | C9 | direct (N × H) |
| 73. C2×D24 | C2×C9 | semidirect |
| 74. C2×#204 | C2×C9 | semidirect |
| 75. #875 | C2×C9 | semidirect |
| 76. #874 | C2×C9 | semidirect |
| 78. C3×#97 | C2×C9 | semidirect |
| 104. C8×C9 | D12 | semidirect |
| 153. #97 | D3×C9 | semidirect |
| 154. C3×C9 | #496 | semidirect |
| 178. C3×C8 | D4×C9 | semidirect |
| 220. C9 | #4712 | direct (N × H) |
| 231. C8 | C9×D12 | semidirect |
| 251. C3 | C9×#496 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C9×D24 | 2 |
| C2×C9×#204 | 2 |
| C9×#875 | 2 |
| C9×#874 | 2 |
| C3×C9×#97 | 2 |
| C3×#4712 | 3 |
| C9×#496 | 3 |