Finite Group DatabasebetaFinite Group DatabasebetaOrder 864.
248 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 248 conjugacy classes of subgroups — too many to draw. Only its 99 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×C9×Dic6 | C2 | semidirect |
| 3. C3×C9×C4⋊C4 | C2 | semidirect |
| 6. C9×Dic3⋊C4 | C2 | semidirect |
| 7. C9×Dic3⋊C4 | C2 | semidirect |
| 31. C9×C4⋊C4 | D3 | semidirect |
| 37. C2×D3×C9 | Q8 | semidirect |
| 45. #896 | C9 | direct (N × H) |
| 74. C2×Dic6 | C2×C9 | semidirect |
| 78. C3×C4⋊C4 | C2×C9 | semidirect |
| 84. Dic3⋊C4 | C2×C9 | semidirect |
| 85. Dic3⋊C4 | C2×C9 | semidirect |
| 111. C3×C9 | C22⋊Q8 | semidirect |
| 148. C4⋊C4 | D3×C9 | semidirect |
| 159. C2×D3 | Q8×C9 | semidirect |
| 177. C9 | #896 | direct (N × H) |
| 209. 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×C4×D3×C9 | 2 |
| C2×C9×Dic6 | 2 |
| C3×C9×C4⋊C4 | 2 |
| C9×(C2×D3)⋊C4 | 2 |
| C9×Dic3⋊C4 | 2 |
| C3×#896 | 3 |
| C9×C22⋊Q8 | 3 |