Finite Group DatabasebetaFinite Group DatabasebetaOrder 864.
458 conjugacy classes of subgroups; only the 120 normal subgroups are shown.
This group has 458 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 |
|---|---|---|
| 3. C3×#3724 | C2 | semidirect |
| 4. C3×Dic32 | C2 | semidirect |
| 6. #63957 | C3 | direct (N × H) |
| 8. C2×C3×C3⋊Dic3 | C4 | semidirect |
| 21. #3724 | C2×C3 | semidirect |
| 22. Dic32 | C2×C3 | semidirect |
| 37. C2×C3⋊Dic3 | C3×C4 | semidirect |
| 89. C33 | #117 | semidirect |
| 155. C32 | #877 | semidirect |
| 156. C32 | C3×#117 | semidirect |
| 186. C3 | #63957 | direct (N × H) |
| 187. C3 | C3×#877 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C3×C3⋊Dic3 | 2 |
| C32×#217 | 2 |
| C3×#3724 | 2 |
| C3×Dic32 | 2 |
| C3×#877 | 3 |
| #63957 | 3 |