Finite Group DatabasebetaFinite Group DatabasebetaOrder 864.
260 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 260 conjugacy classes of subgroups — too many to draw. Only its 105 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 |
| 4. C9×C4⋊Dic3 | C2 | semidirect |
| 5. C9×Dic3⋊C4 | C2 | semidirect |
| 21. C2×Q8×C9 | D3 | semidirect |
| 29. C2×D3×C9 | Q8 | semidirect |
| 35. #946 | C9 | direct (N × H) |
| 58. C2×C3×Q8 | C2×C9 | semidirect |
| 66. C4⋊Dic3 | C2×C9 | semidirect |
| 67. Dic3⋊C4 | C2×C9 | semidirect |
| 88. C3×C9 | C22⋊Q8 | semidirect |
| 117. C2×Q8 | D3×C9 | semidirect |
| 130. C2×D3 | Q8×C9 | semidirect |
| 143. C9 | #946 | direct (N × H) |
| 171. C3 | C9×C22⋊Q8 | semidirect |
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×C4×D3×C9 | 2 |
| C9×(C2×D3)⋊C4 | 2 |
| C9×C4⋊Dic3 | 2 |
| C9×Dic3⋊C4 | 2 |
| C3×#946 | 3 |
| C9×C22⋊Q8 | 3 |