Finite Group DatabasebetaFinite Group DatabasebetaOrder 864.
506 conjugacy classes of subgroups; only the 291 normal subgroups are shown.
This group has 506 conjugacy classes of subgroups — too many to draw. Only its 291 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 |
| 2. D3×Q8×C9 | C2 | direct (N × H) |
| 4. C2×C9×Dic6 | C2 | semidirect |
| 8. C3×Q8×C9 | C22 | semidirect |
| 12. C9×Dic6 | C22 | semidirect |
| 20. C2×Q8×C9 | D3 | direct (N × H) |
| 23. C2×D3×C9 | Q8 | direct (N × H) |
| 28. C2×D3×Q8 | C9 | direct (N × H) |
| 38. Q8×C9 | C2×D3 | direct (N × H) |
| 43. C2×C3×C9 | C2×Q8 | semidirect |
| 45. D3×C9 | C2×Q8 | direct (N × H) |
| 49. C2×C3×Q8 | C2×C9 | semidirect |
| 52. D3×Q8 | C2×C9 | direct (N × H) |
| 54. C2×Dic6 | C2×C9 | semidirect |
| 68. C3×C9 | C22×Q8 | semidirect |
| 73. C3×Q8 | C22×C9 | semidirect |
| 82. Dic6 | C22×C9 | semidirect |
| 89. C2×C9 | D3×Q8 | direct (N × H) |
| 93. C2×Q8 | D3×C9 | direct (N × H) |
| 100. C2×D3 | Q8×C9 | direct (N × H) |
| 109. C9 | C2×D3×Q8 | direct (N × H) |
| 112. Q8 | C2×D3×C9 | direct (N × H) |
| 119. C2×C3 | C2×Q8×C9 | semidirect |
| 123. D3 | C2×Q8×C9 | direct (N × H) |
| 130. C3 | C22×Q8×C9 | semidirect |
| 133. C2 | D3×Q8×C9 | 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 |
| D3×Q8×C9 | 2 |
| C2×C4×D3×C9 | 2 |
| C2×C9×Dic6 | 2 |
| C2×C3×D3×Q8 | 3 |
| C22×Q8×C9 | 3 |