Finite Group DatabasebetaFinite Group DatabasebetaOrder 864.
266 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 266 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×Q8×C9 | C2 | semidirect |
| 3. C9×(C2×D3)⋊C4 | C2 | semidirect |
| 4. C4×C9×Dic3 | C2 | semidirect |
| 18. C2×Q8×C9 | D3 | semidirect |
| 29. #947 | C9 | direct (N × H) |
| 49. C2×C3×Q8 | C2×C9 | semidirect |
| 55. (C2×D3)⋊C4 | C2×C9 | semidirect |
| 56. C4×Dic3 | C2×C9 | semidirect |
| 73. C3×C9 | #124 | semidirect |
| 97. C2×Q8 | D3×C9 | semidirect |
| 118. C9 | #947 | direct (N × H) |
| 140. C3 | C9×#124 | 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 |
| C2×C9×D12 | 2 |
| C9×(C2×D3)⋊C4 | 2 |
| C4×C9×Dic3 | 2 |
| C3×#947 | 3 |
| C9×#124 | 3 |