Finite Group DatabasebetaFinite Group DatabasebetaOrder 864.
258 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 258 conjugacy classes of subgroups — too many to draw. Only its 87 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. C9×#235 | C2 | semidirect |
| 3. C9×#214 | C2 | semidirect |
| 4. C9×#213 | C2 | semidirect |
| 5. C9×#208 | C2 | semidirect |
| 13. C9×D12 | C22 | semidirect |
| 15. C9×Dic6 | C22 | semidirect |
| 16. C9×C3⋊C8 | C22 | semidirect |
| 24. C2×D4×C9 | D3 | semidirect |
| 36. #932 | C9 | direct (N × H) |
| 65. C2×C3×D4 | C2×C9 | semidirect |
| 67. #235 | C2×C9 | semidirect |
| 71. #214 | C2×C9 | semidirect |
| 72. #213 | C2×C9 | semidirect |
| 73. #208 | C2×C9 | semidirect |
| 94. C3×C9 | AGL(1,ℤ/8) | semidirect |
| 112. D12 | C22×C9 | semidirect |
| 114. Dic6 | C22×C9 | semidirect |
| 116. C3⋊C8 | C22×C9 | semidirect |
| 129. C2×D4 | D3×C9 | semidirect |
| 154. C9 | #932 | direct (N × H) |
| 183. C3 | C9×AGL(1,ℤ/8) | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×D4×C9 | 2 |
| C9×#235 | 2 |
| C9×#214 | 2 |
| C9×#213 | 2 |
| C9×#208 | 2 |
| C3×#932 | 3 |
| C9×AGL(1,ℤ/8) | 3 |