Finite Group DatabasebetaFinite Group DatabasebetaOrder 864.
242 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 242 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×#215 | C2 | direct (N × H) |
| 4. C2×C9×C3⋊C8 | C2 | semidirect |
| 9. C3×Q8×C9 | C22 | semidirect |
| 14. C9×C3⋊C8 | C22 | semidirect |
| 20. C2×Q8×C9 | D3 | semidirect |
| 31. C2×#215 | C9 | direct (N × H) |
| 44. Q8×C9 | C2×D3 | semidirect |
| 52. C2×C3×C9 | SD16 | semidirect |
| 56. C2×C3×Q8 | C2×C9 | semidirect |
| 62. #215 | C2×C9 | direct (N × H) |
| 63. C2×C3⋊C8 | C2×C9 | semidirect |
| 81. C3×C9 | C2×SD16 | semidirect |
| 88. C3×Q8 | C22×C9 | semidirect |
| 101. C3⋊C8 | C22×C9 | semidirect |
| 108. C2×C9 | #215 | direct (N × H) |
| 110. C2×Q8 | D3×C9 | semidirect |
| 132. C9 | C2×#215 | direct (N × H) |
| 135. Q8 | C2×D3×C9 | semidirect |
| 144. C2×C3 | C9×SD16 | semidirect |
| 156. C3 | C2×C9×SD16 | semidirect |
| 159. C2 | C9×#215 | direct (N × H) |
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×#215 | 2 |
| C2×C9×C3⋊C8 | 2 |
| C2×C3×#215 | 3 |
| C2×C9×SD16 | 3 |