Finite Group DatabasebetaFinite Group DatabasebetaOrder 864.
506 conjugacy classes of subgroups; only the 147 normal subgroups are shown.
This group has 506 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 |
|---|---|---|
| 1. Q8×C3⋊D9 | C2 | semidirect |
| 2. D3×Q8×C9 | C2 | semidirect |
| 3. C3×Q8×D9 | C2 | semidirect |
| 5. D3×Dic18 | C2 | semidirect |
| 6. (C3⋊D9)⋊Q8 | C2 | semidirect |
| 7. D9×Dic6 | C2 | semidirect |
| 11. C3×Q8×C9 | C22 | semidirect |
| 13. #6226 | C22 | semidirect |
| 16. C9×Dic6 | C22 | semidirect |
| 17. C3×Dic18 | C22 | semidirect |
| 21. #6189 | C22 | semidirect |
| 34. Q8×D9 | D3 | direct (N × H) |
| 40. D3×D9 | Q8 | direct (N × H) |
| 62. Q8×C9 | C2×D3 | semidirect |
| 73. Dic18 | C2×D3 | semidirect |
| 75. C3⋊D9 | C2×Q8 | semidirect |
| 76. D3×C9 | C2×Q8 | semidirect |
| 77. C3×D9 | C2×Q8 | semidirect |
| 88. D3×Q8 | D9 | direct (N × H) |
| 113. C3×C9 | C22×Q8 | semidirect |
| 119. C3×Q8 | C2×D9 | semidirect |
| 140. Dic6 | C2×D9 | semidirect |
| 150. D9 | D3×Q8 | direct (N × H) |
| 179. C9 | C2×D3×Q8 | semidirect |
| 185. Q8 | D3×D9 | direct (N × H) |
| 201. D3 | Q8×D9 | direct (N × H) |
| 211. C3 | C2×Q8×D9 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q8×C3⋊D9 | 2 |
| D3×Q8×C9 | 2 |
| C3×Q8×D9 | 2 |
| C4×D3×D9 | 2 |
| D3×Dic18 | 2 |
| (C3⋊D9)⋊Q8 | 2 |
| D9×Dic6 | 2 |
| D32×Q8 | 3 |
| C2×Q8×D9 | 3 |