Finite Group DatabasebetaFinite Group DatabasebetaOrder 864.
250 conjugacy classes of subgroups; only the 147 normal subgroups are shown.
This group has 250 conjugacy classes of subgroups — too many to draw. Only its 147 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 |
|---|---|---|
| 2. C2×C3×C8×C9 | C2 | semidirect |
| 3. C2×C9×C3⋊C8 | C2 | semidirect |
| 4. D3×C8×C9 | C2 | direct (N × H) |
| 12. C3×C8×C9 | C22 | semidirect |
| 13. C9×C3⋊C8 | C22 | semidirect |
| 22. C2×C8×C9 | D3 | direct (N × H) |
| 24. C2×D3×C9 | C8 | direct (N × H) |
| 30. C2×D3×C8 | C9 | direct (N × H) |
| 46. C8×C9 | C2×D3 | direct (N × H) |
| 47. C2×C3×C9 | C2×C8 | semidirect |
| 49. D3×C9 | C2×C8 | direct (N × H) |
| 55. C2×C3×C8 | C2×C9 | semidirect |
| 57. C2×C3⋊C8 | C2×C9 | semidirect |
| 58. D3×C8 | C2×C9 | direct (N × H) |
| 75. C3×C9 | C22×C8 | semidirect |
| 89. C3×C8 | C22×C9 | semidirect |
| 91. C3⋊C8 | C22×C9 | semidirect |
| 98. C2×C9 | D3×C8 | direct (N × H) |
| 103. C2×C8 | D3×C9 | direct (N × H) |
| 109. C2×D3 | C8×C9 | direct (N × H) |
| 121. C9 | C2×D3×C8 | direct (N × H) |
| 128. C8 | C2×D3×C9 | direct (N × H) |
| 132. C2×C3 | C2×C8×C9 | semidirect |
| 136. D3 | C2×C8×C9 | direct (N × H) |
| 144. C3 | C22×C8×C9 | semidirect |
| 147. C2 | D3×C8×C9 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×D3×C9 | 2 |
| C2×C3×C8×C9 | 2 |
| C2×C9×C3⋊C8 | 2 |
| D3×C8×C9 | 2 |
| C2×C3×D3×C8 | 3 |
| C22×C8×C9 | 3 |