Finite Group DatabasebetaFinite Group DatabasebetaOrder 864.
586 conjugacy classes of subgroups; only the 120 normal subgroups are shown.
This group has 586 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×C4⋊(C3⋊D3) | C2 | semidirect |
| 2. C2×C32×D12 | C2 | semidirect |
| 3. C2×C3×#626 | C2 | semidirect |
| 4. C32×C4×Dic3 | C2 | semidirect |
| 7. #63911 | C3 | direct (N × H) |
| 16. C2×C4⋊(C3⋊D3) | C2×C3 | semidirect |
| 23. C2×C3×D12 | D3 | semidirect |
| 24. C2×C3×D12 | C2×C3 | semidirect |
| 25. C2×#626 | C2×C3 | semidirect |
| 28. C3×C4×Dic3 | D3 | semidirect |
| 29. C3×C4×Dic3 | C2×C3 | semidirect |
| 35. C33×C4 | D4 | semidirect |
| 36. C32×Dic3 | D4 | semidirect |
| 84. C2×D12 | C3×D3 | semidirect |
| 88. C4×Dic3 | C3×D3 | semidirect |
| 117. C32×C4 | D12 | semidirect |
| 118. C32×C4 | #67 | semidirect |
| 119. C32×C4 | C3×D4 | semidirect |
| 121. C3×Dic3 | D12 | semidirect |
| 122. C3×Dic3 | C3×D4 | semidirect |
| 124. C33 | #127 | semidirect |
| 211. C3×C4 | #626 | semidirect |
| 212. C3×C4 | C3×D12 | semidirect |
| 213. C3×C4 | C3×#67 | semidirect |
| 214. Dic3 | C3×D12 | semidirect |
| 219. C32 | #874 | semidirect |
| 220. C32 | #940 | semidirect |
| 221. C32 | C3×#127 | semidirect |
| 257. C4 | C3×#626 | semidirect |
| 262. C3 | #63911 | direct (N × H) |
| 263. C3 | C3×#874 | semidirect |
| 264. C3 | C3×#940 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×C4⋊(C3⋊D3) | 2 |
| C2×C32×D12 | 2 |
| C2×C3×#626 | 2 |
| C32×C4×Dic3 | 2 |
| C3×#940 | 3 |
| C3×#874 | 3 |
| #63911 | 3 |