Finite Group DatabasebetaFinite Group DatabasebetaOrder 864.
316 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 316 conjugacy classes of subgroups — too many to draw. Only its 99 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×#67 | C2 | semidirect |
| 2. C2×C9×#67 | C2 | semidirect |
| 3. C2×C9×D12 | C2 | semidirect |
| 4. C2×C4×D3×C9 | C2 | semidirect |
| 5. C3×C9×C22⋊C4 | C2 | semidirect |
| 6. C9×(C2×D3)⋊C4 | C2 | semidirect |
| 7. C9×Dic3⋊C4 | C2 | semidirect |
| 35. C9×C22⋊C4 | D3 | semidirect |
| 45. C2×D3×C9 | D4 | semidirect |
| 49. C9×Dic3 | D4 | semidirect |
| 51. #884 | C9 | direct (N × H) |
| 87. C2×#67 | C2×C9 | semidirect |
| 88. C2×#67 | C2×C9 | semidirect |
| 89. C2×D12 | C2×C9 | semidirect |
| 90. C2×C4×D3 | C2×C9 | semidirect |
| 94. C3×C22⋊C4 | C2×C9 | semidirect |
| 96. (C2×D3)⋊C4 | C2×C9 | semidirect |
| 97. Dic3⋊C4 | C2×C9 | semidirect |
| 133. C3×C9 | #121 | semidirect |
| 181. C22⋊C4 | D3×C9 | semidirect |
| 205. C2×D3 | D4×C9 | semidirect |
| 215. Dic3 | D4×C9 | semidirect |
| 218. C9 | #884 | direct (N × H) |
| 261. C3 | C9×#121 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C9×#67 | 2 |
| C2×C9×D12 | 2 |
| C2×C4×D3×C9 | 2 |
| C3×C9×C22⋊C4 | 2 |
| C9×(C2×D3)⋊C4 | 2 |
| C9×Dic3⋊C4 | 2 |
| C3×#884 | 3 |
| C9×#121 | 3 |