Finite Group DatabasebetaFinite Group DatabasebetaOrder 864.
458 conjugacy classes of subgroups; only the 136 normal subgroups are shown.
This group has 458 conjugacy classes of subgroups — too many to draw. Only its 136 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 |
|---|---|---|
| 4. C3×Dic3⋊Dic3 | C2 | semidirect |
| 5. C3×Dic32 | C2 | semidirect |
| 8. #63955 | C3 | direct (N × H) |
| 11. C2×C32×Dic3 | C4 | semidirect |
| 31. Dic3⋊Dic3 | C2×C3 | semidirect |
| 32. Dic32 | C2×C3 | semidirect |
| 62. C2×C3×Dic3 | Dic3 | semidirect |
| 63. C2×C3×Dic3 | C3×C4 | semidirect |
| 129. C33 | #117 | semidirect |
| 153. C2×Dic3 | C3×Dic3 | semidirect |
| 224. C32 | #877 | semidirect |
| 225. C32 | #926 | semidirect |
| 226. C32 | C3×#117 | semidirect |
| 265. C3 | #63955 | direct (N × H) |
| 266. C3 | C3×#877 | semidirect |
| 267. C3 | C3×#926 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C32×Dic3 | 2 |
| C3×#3757 | 2 |
| C32×#217 | 2 |
| C3×Dic3⋊Dic3 | 2 |
| C3×Dic32 | 2 |
| C3×#926 | 3 |
| C3×#877 | 3 |
| #63955 | 3 |