Finite Group DatabasebetaFinite Group DatabasebetaOrder 864.
478 conjugacy classes of subgroups; only the 255 normal subgroups are shown.
This group has 478 conjugacy classes of subgroups — too many to draw. Only its 255 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×#41 | C2 | semidirect |
| 2. D3×Q8×C9 | C2 | semidirect |
| 3. C9×#237 | C2 | semidirect |
| 4. C9×#235 | C2 | semidirect |
| 5. C2×C9×Dic6 | C2 | semidirect |
| 25. C9×#41 | D3 | semidirect |
| 34. #1010 | C9 | direct (N × H) |
| 62. C3×#41 | C2×C9 | semidirect |
| 66. D3×Q8 | C2×C9 | semidirect |
| 67. #237 | C2×C9 | semidirect |
| 68. #235 | C2×C9 | semidirect |
| 69. C2×Dic6 | C2×C9 | semidirect |
| 84. C3×C9 | 2−1+4 | semidirect |
| 116. #41 | D3×C9 | semidirect |
| 134. C9 | #1010 | direct (N × H) |
| 158. C3 | C9×2−1+4 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C9×#41 | 2 |
| D3×Q8×C9 | 2 |
| C9×#237 | 2 |
| C9×#235 | 2 |
| C2×C9×Dic6 | 2 |
| C3×#1010 | 3 |
| C9×2−1+4 | 3 |