Finite Group DatabasebetaFinite Group DatabasebetaOrder 864.
660 conjugacy classes of subgroups; only the 130 normal subgroups are shown.
This group has 660 conjugacy classes of subgroups — too many to draw. Only its 130 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 |
|---|---|---|
| 2. C2×C3×#634 | C2 | semidirect |
| 3. C32×C4⋊Dic3 | C2 | semidirect |
| 4. Dic3⋊(C3⋊Dic3) | C2 | semidirect |
| 18. C2×#634 | D3 | semidirect |
| 23. C3×C4⋊Dic3 | D3 | semidirect |
| 29. C2×C3⋊(C3⋊D3) | Q8 | semidirect |
| 67. C4⋊Dic3 | C3⋊D3 | semidirect |
| 92. C33 | C22⋊Q8 | semidirect |
| 151. C32 | #897 | semidirect |
| 152. C32 | #946 | semidirect |
| 181. C3 | #63871 | semidirect |
| 182. C3 | #64106 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×C3⋊(C3⋊D3) | 2 |
| C2×C3×#634 | 2 |
| C32×C4⋊Dic3 | 2 |
| Dic3⋊(C3⋊Dic3) | 2 |
| #88804 | 2 |
| #64106 | 3 |
| #63871 | 3 |