Finite Group DatabasebetaFinite Group DatabasebetaOrder 864.
282 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 282 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×C3×D4×C9 | C2 | semidirect |
| 2. C2×C9×D12 | C2 | semidirect |
| 3. C9×#213 | C2 | direct (N × H) |
| 4. C2×C9×C3⋊C8 | C2 | semidirect |
| 10. C3×D4×C9 | C22 | semidirect |
| 13. C9×D12 | C22 | semidirect |
| 14. C9×C3⋊C8 | C22 | semidirect |
| 21. C2×D4×C9 | D3 | semidirect |
| 32. C2×#213 | C9 | direct (N × H) |
| 49. D4×C9 | C2×D3 | semidirect |
| 54. C2×C3×C9 | D8 | semidirect |
| 59. C2×C3×D4 | C2×C9 | semidirect |
| 61. C2×D12 | C2×C9 | semidirect |
| 64. #213 | C2×C9 | direct (N × H) |
| 65. C2×C3⋊C8 | C2×C9 | semidirect |
| 86. C3×C9 | C2×D8 | semidirect |
| 98. C3×D4 | C22×C9 | semidirect |
| 104. D12 | C22×C9 | semidirect |
| 106. C3⋊C8 | C22×C9 | semidirect |
| 116. C2×C9 | #213 | direct (N × H) |
| 119. C2×D4 | D3×C9 | semidirect |
| 143. C9 | C2×#213 | direct (N × H) |
| 149. D4 | C2×D3×C9 | semidirect |
| 158. C2×C3 | C9×D8 | semidirect |
| 171. C3 | C2×C9×D8 | semidirect |
| 175. C2 | C9×#213 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×D4×C9 | 2 |
| C2×C9×D12 | 2 |
| C9×#213 | 2 |
| C2×C9×C3⋊C8 | 2 |
| C2×C3×#213 | 3 |
| C2×C9×D8 | 3 |