Finite Group DatabasebetaFinite Group DatabasebetaOrder 864.
336 conjugacy classes of subgroups; only the 116 normal subgroups are shown.
This group has 336 conjugacy classes of subgroups — too many to draw. Only its 116 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. C22×C3×C4×C9 | C2 | semidirect |
| 3. C2×C3×C4×D9 | C2 | semidirect |
| 4. C3×#3676 | C2 | semidirect |
| 5. C3×(C2×D9)⋊C4 | C2 | semidirect |
| 6. C3×Dic9⋊C4 | C2 | semidirect |
| 7. C3×C4×Dic9 | C2 | semidirect |
| 9. C4×#611 | C3 | direct (N × H) |
| 15. C3×#611 | C4 | direct (N × H) |
| 28. C22×C4×C9 | C2×C3 | semidirect |
| 30. C2×C4×D9 | C2×C3 | semidirect |
| 31. #3676 | C2×C3 | semidirect |
| 32. (C2×D9)⋊C4 | C2×C3 | semidirect |
| 33. Dic9⋊C4 | C2×C3 | semidirect |
| 34. C4×Dic9 | C2×C3 | semidirect |
| 37. C22×C3×C9 | C2×C4 | semidirect |
| 41. C2×C3×D9 | C2×C4 | semidirect |
| 43. C3×C4×C9 | D4 | semidirect |
| 46. C3×Dic9 | C2×C4 | semidirect |
| 68. #611 | C3×C4 | direct (N × H) |
| 81. C22×C3×C4 | D9 | semidirect |
| 111. C22×C9 | C2×C3×C4 | semidirect |
| 115. C2×D9 | C2×C3×C4 | semidirect |
| 119. C4×C9 | C3×D4 | semidirect |
| 122. Dic9 | C2×C3×C4 | semidirect |
| 124. C3×C9 | C4×D4 | semidirect |
| 165. C22×C4 | C3×D9 | semidirect |
| 181. C22×C3 | C4×D9 | semidirect |
| 195. C3×C4 | #611 | direct (N × H) |
| 202. C9 | C3×C4×D4 | semidirect |
| 232. C22 | C3×C4×D9 | semidirect |
| 238. C4 | C3×#611 | direct (N × H) |
| 240. C3 | C4×#611 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C3×C4×C9 | 2 |
| C2×C3×#611 | 2 |
| C2×C3×C4×D9 | 2 |
| C3×#3676 | 2 |
| C3×(C2×D9)⋊C4 | 2 |
| C3×Dic9⋊C4 | 2 |
| C3×C4×Dic9 | 2 |
| C3×C4×#67 | 3 |
| C4×#611 | 3 |