Finite Group DatabasebetaFinite Group DatabasebetaOrder 864.
700 conjugacy classes of subgroups; only the 138 normal subgroups are shown.
This group has 700 conjugacy classes of subgroups — too many to draw. Only its 138 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×#6289 | C2 | semidirect |
| 3. C2×Dic3×C3⋊D3 | C2 | semidirect |
| 4. #88859 | C2 | semidirect |
| 5. C3×#3752 | C2 | semidirect |
| 6. C32×C4×Dic3 | C2 | semidirect |
| 7. Dic3⋊(C3⋊Dic3) | C2 | semidirect |
| 17. #6292 | C4 | semidirect |
| 30. #3752 | D3 | semidirect |
| 33. C3×C4×Dic3 | D3 | semidirect |
| 38. C2×C3⋊(C3⋊D3) | C2×C4 | semidirect |
| 41. C2×C3×C3⋊D3 | C2×C4 | semidirect |
| 45. C32×Dic3 | C2×C4 | semidirect |
| 46. C32×Dic3 | D4 | semidirect |
| 91. C4×Dic3 | C3⋊D3 | semidirect |
| 106. C2×C3⋊D3 | C4×D3 | semidirect |
| 120. C3×Dic3 | C4×D3 | semidirect |
| 121. C3×Dic3 | D12 | semidirect |
| 123. C33 | C4×D4 | semidirect |
| 196. Dic3 | C4×C3⋊D3 | semidirect |
| 197. Dic3 | C4⋊(C3⋊D3) | semidirect |
| 199. C32 | C4×D12 | semidirect |
| 200. C32 | #67⋊C4 | semidirect |
| 238. C3 | #63880 | semidirect |
| 239. C3 | C4×C4⋊(C3⋊D3) | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#6292 | 2 |
| C2×#6289 | 2 |
| C2×Dic3×C3⋊D3 | 2 |
| #88859 | 2 |
| C3×#3752 | 2 |
| C32×C4×Dic3 | 2 |
| Dic3⋊(C3⋊Dic3) | 2 |
| C4×C4⋊(C3⋊D3) | 3 |
| #63880 | 3 |