Finite Group DatabasebetaFinite Group DatabasebetaOrder 864.
336 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 336 conjugacy classes of subgroups — too many to draw. Only its 105 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×D4×C9 | C2 | semidirect |
| 2. C2×C9×#67 | C2 | semidirect |
| 3. C2×C9×#67 | C2 | semidirect |
| 4. C22×C9×Dic3 | C2 | semidirect |
| 5. C9×#217 | C2 | semidirect |
| 6. C9×(C2×D3)⋊C4 | C2 | semidirect |
| 7. C9×Dic3⋊C4 | C2 | semidirect |
| 31. C2×D4×C9 | D3 | semidirect |
| 41. C22×C3×C9 | D4 | semidirect |
| 49. C9×Dic3 | D4 | semidirect |
| 51. #939 | C9 | direct (N × H) |
| 87. C2×C3×D4 | C2×C9 | semidirect |
| 90. C2×#67 | C2×C9 | semidirect |
| 91. C2×#67 | C2×C9 | semidirect |
| 92. C22×Dic3 | C2×C9 | semidirect |
| 96. #217 | C2×C9 | semidirect |
| 97. (C2×D3)⋊C4 | C2×C9 | semidirect |
| 98. Dic3⋊C4 | C2×C9 | semidirect |
| 128. C22×C9 | #67 | semidirect |
| 136. C3×C9 | #121 | semidirect |
| 182. C2×D4 | D3×C9 | semidirect |
| 207. C22×C3 | D4×C9 | semidirect |
| 222. Dic3 | D4×C9 | semidirect |
| 225. C9 | #939 | direct (N × H) |
| 262. C22 | C9×#67 | semidirect |
| 269. C3 | C9×#121 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×D4×C9 | 2 |
| C2×C9×#67 | 2 |
| C22×C9×Dic3 | 2 |
| C9×#217 | 2 |
| C9×(C2×D3)⋊C4 | 2 |
| C9×Dic3⋊C4 | 2 |
| C3×#939 | 3 |
| C9×#121 | 3 |