Finite Group DatabasebetaFinite Group DatabasebetaOrder 864.
394 conjugacy classes of subgroups; only the 120 normal subgroups are shown.
This group has 394 conjugacy classes of subgroups — too many to draw. Only its 120 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 |
|---|---|---|
| 7. #63866 | C3 | direct (N × H) |
| 33. C32×Dic3 | Q8 | semidirect |
| 105. C3×Dic3 | Dic6 | semidirect |
| 106. C3×Dic3 | C3×Q8 | semidirect |
| 108. C33 | C4⋊Q8 | semidirect |
| 179. Dic3 | C3×Dic6 | semidirect |
| 184. C32 | #869 | semidirect |
| 185. C32 | #944 | semidirect |
| 186. C32 | C3×C4⋊Q8 | semidirect |
| 216. C3 | #63866 | direct (N × H) |
| 217. C3 | C3×#869 | semidirect |
| 218. C3 | C3×#944 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×#634 | 2 |
| C2×C32×Dic6 | 2 |
| C32×C4×Dic3 | 2 |
| C3×Dic3⋊Dic3 | 2 |
| C3×#944 | 3 |
| C3×#869 | 3 |
| #63866 | 3 |