Finite Group DatabasebetaFinite Group DatabasebetaOrder 864.
198 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 198 conjugacy classes of subgroups — too many to draw. Only its 87 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. C3×C9×Q16 | C2 | semidirect |
| 3. C9×#216 | C2 | semidirect |
| 4. C9×Dic12 | C2 | semidirect |
| 24. C9×Q16 | D3 | direct (N × H) |
| 32. D3×Q16 | C9 | direct (N × H) |
| 50. D3×C9 | Q16 | direct (N × H) |
| 56. C3×Q16 | C2×C9 | semidirect |
| 59. #216 | C2×C9 | semidirect |
| 60. Dic12 | C2×C9 | semidirect |
| 75. C3×C9 | C2×Q16 | semidirect |
| 100. Q16 | D3×C9 | direct (N × H) |
| 116. C9 | D3×Q16 | direct (N × H) |
| 128. D3 | C9×Q16 | direct (N × H) |
| 135. C3 | C2×C9×Q16 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D3×Q8×C9 | 2 |
| C3×C9×Q16 | 2 |
| C9×#216 | 2 |
| C9×Dic12 | 2 |
| D3×C8×C9 | 2 |
| C3×D3×Q16 | 3 |
| C2×C9×Q16 | 3 |