Finite Group DatabasebetaFinite Group DatabasebetaOrder 864.
548 conjugacy classes of subgroups; only the 120 normal subgroups are shown.
This group has 548 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 |
|---|---|---|
| 1. C2×C3×#634 | C2 | semidirect |
| 3. #88857 | C2 | semidirect |
| 5. #88807 | C2 | semidirect |
| 6. Dic3⋊(C3⋊Dic3) | C2 | semidirect |
| 20. C2×#634 | D3 | semidirect |
| 37. C2×C32×D3 | Q8 | semidirect |
| 94. C2×C3×D3 | Dic6 | semidirect |
| 111. C33 | C22⋊Q8 | semidirect |
| 159. C2×D3 | #634 | semidirect |
| 176. C32 | #878 | semidirect |
| 177. C32 | #946 | semidirect |
| 209. C3 | #63887 | semidirect |
| 210. C3 | #64087 | 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×D3×C3⋊Dic3 | 2 |
| #88857 | 2 |
| C32×(C2×D3)⋊C4 | 2 |
| #88807 | 2 |
| Dic3⋊(C3⋊Dic3) | 2 |
| (C2×D3)⋊(C3⋊Dic3) | 2 |
| #64087 | 3 |
| #63887 | 3 |