Finite Group DatabasebetaFinite Group DatabasebetaOrder 864.
230 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 230 conjugacy classes of subgroups — too many to draw. Only its 79 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 |
|---|---|---|
| 26. C3×C4×C9 | Q8 | semidirect |
| 30. C3×Dic9 | Q8 | semidirect |
| 71. C4×C9 | Dic6 | semidirect |
| 74. Dic9 | Dic6 | semidirect |
| 77. C3×C9 | C4⋊Q8 | semidirect |
| 113. C3×C4 | Dic18 | semidirect |
| 123. C9 | #869 | semidirect |
| 144. C4 | #6189 | semidirect |
| 146. C3 | #63450 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#6189 | 2 |
| C4⋊(C3⋊Dic9) | 2 |
| C9×C4⋊Dic3 | 2 |
| C3×C4×Dic9 | 2 |
| Dic9⋊Dic3 | 2 |
| #63918 | 3 |
| #63450 | 3 |