Finite Group DatabasebetaFinite Group DatabasebetaOrder 864.
780 conjugacy classes of subgroups; only the 210 normal subgroups are shown.
This group has 780 conjugacy classes of subgroups — too many to draw. Only its 210 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×C33×D4 | C2 | semidirect |
| 2. C2×C32×#67 | C2 | semidirect |
| 3. C2×C32×#67 | C2 | semidirect |
| 4. C22×C32×Dic3 | C2 | semidirect |
| 5. C32×#217 | C2 | semidirect |
| 6. C32×(C2×D3)⋊C4 | C2 | semidirect |
| 7. C32×Dic3⋊C4 | C2 | semidirect |
| 9. C3×#939 | C3 | direct (N × H) |
| 24. C2×C32×D4 | D3 | semidirect |
| 25. C2×C32×D4 | C2×C3 | semidirect |
| 27. C2×C3×#67 | C2×C3 | semidirect |
| 28. C2×C3×#67 | C2×C3 | semidirect |
| 29. C22×C3×Dic3 | C2×C3 | semidirect |
| 33. C3×#217 | C2×C3 | semidirect |
| 34. C3×(C2×D3)⋊C4 | C2×C3 | semidirect |
| 35. C3×Dic3⋊C4 | C2×C3 | semidirect |
| 41. C22×C33 | D4 | semidirect |
| 49. C32×Dic3 | D4 | semidirect |
| 51. #939 | C32 | direct (N × H) |
| 87. C2×C3×D4 | C3×D3 | semidirect |
| 88. C2×C3×D4 | C2×C32 | semidirect |
| 90. C2×#67 | C2×C32 | semidirect |
| 91. C2×#67 | C2×C32 | semidirect |
| 92. C22×Dic3 | C2×C32 | semidirect |
| 96. #217 | C2×C32 | semidirect |
| 97. (C2×D3)⋊C4 | C2×C32 | semidirect |
| 98. Dic3⋊C4 | C2×C32 | semidirect |
| 119. C22×C32 | #67 | semidirect |
| 120. C22×C32 | C3×D4 | semidirect |
| 134. C3×Dic3 | C3×D4 | semidirect |
| 136. C33 | #121 | semidirect |
| 182. C2×D4 | C32×D3 | semidirect |
| 207. C22×C3 | C3×#67 | semidirect |
| 208. C22×C3 | C32×D4 | semidirect |
| 222. Dic3 | C32×D4 | semidirect |
| 224. C32 | #939 | direct (N × H) |
| 225. C32 | C3×#121 | semidirect |
| 262. C22 | C32×#67 | semidirect |
| 269. C3 | C3×#939 | direct (N × H) |
| 270. C3 | C32×#121 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C33×D4 | 2 |
| C2×C32×#67 | 2 |
| C22×C32×Dic3 | 2 |
| C32×#217 | 2 |
| C32×(C2×D3)⋊C4 | 2 |
| C32×Dic3⋊C4 | 2 |
| C32×#121 | 3 |
| C3×#939 | 3 |