Finite Group DatabasebetaFinite Group DatabasebetaOrder 864.
524 conjugacy classes of subgroups; only the 156 normal subgroups are shown.
This group has 524 conjugacy classes of subgroups — too many to draw. Only its 156 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 |
|---|---|---|
| 11. C3×#634 | C4 | semidirect |
| 30. C32×Dic3 | Q8 | semidirect |
| 42. #634 | Dic3 | direct (N × H) |
| 75. C3×Dic3 | Dic6 | semidirect |
| 77. C33 | C4×Q8 | semidirect |
| 120. Dic3 | #634 | direct (N × H) |
| 122. C32 | C4×Dic6 | semidirect |
| 123. C32 | Q8×Dic3 | semidirect |
| 146. C3 | Dic3×Dic6 | semidirect |
| 147. C3 | C4×#634 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×#634 | 2 |
| C4⋊(C3⋊(C3⋊Dic3)) | 2 |
| C32×C4×Dic3 | 2 |
| #88807 | 2 |
| Dic3×C3⋊Dic3 | 2 |
| C4×#634 | 3 |
| Dic3×Dic6 | 3 |