Finite Group DatabasebetaFinite Group DatabasebetaOrder 864.
218 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 218 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×Q8×C9 | C2 | semidirect |
| 3. C9×#216 | C2 | semidirect |
| 4. C9×#215 | C2 | semidirect |
| 5. C9×#208 | C2 | semidirect |
| 24. C2×Q8×C9 | D3 | semidirect |
| 35. #942 | C9 | direct (N × H) |
| 63. C2×C3×Q8 | C2×C9 | semidirect |
| 69. #216 | C2×C9 | semidirect |
| 70. #215 | C2×C9 | semidirect |
| 71. #208 | C2×C9 | semidirect |
| 89. C3×C9 | #137 | semidirect |
| 121. C2×Q8 | D3×C9 | semidirect |
| 143. C9 | #942 | direct (N × H) |
| 168. C3 | C9×#137 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×Q8×C9 | 2 |
| C9×#235 | 2 |
| C9×#216 | 2 |
| C9×#215 | 2 |
| C9×#208 | 2 |
| C3×#942 | 3 |
| C9×#137 | 3 |