Finite Group DatabasebetaFinite Group DatabasebetaOrder 864.
460 conjugacy classes of subgroups; only the 281 normal subgroups are shown.
This group has 460 conjugacy classes of subgroups — too many to draw. Only its 281 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 |
|---|---|---|
| 3. C4⋊(C3⋊Dic9) | C2 | direct (N × H) |
| 7. C2×C3×C4×C9 | C4 | semidirect |
| 21. C3×C4×C9 | C2×C4 | semidirect |
| 31. C2×C4×C9 | Dic3 | semidirect |
| 35. C2×C3×C9 | C4⋊C4 | semidirect |
| 55. C4×C9 | C2×Dic3 | semidirect |
| 58. C3×C9 | C2×C4⋊C4 | semidirect |
| 61. C2×C3×C4 | Dic9 | semidirect |
| 73. C2×C9 | C4⋊Dic3 | semidirect |
| 88. C3×C4 | C2×Dic9 | semidirect |
| 93. C9 | C2×C4⋊Dic3 | semidirect |
| 97. C2×C4 | C3⋊Dic9 | semidirect |
| 99. C2×C3 | C4⋊Dic9 | semidirect |
| 112. C4 | C2×C3⋊Dic9 | semidirect |
| 113. C3 | C2×C4⋊Dic9 | semidirect |
| 115. C2 | C4⋊(C3⋊Dic9) | 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 |
| C22×C3⋊Dic9 | 2 |
| C4⋊(C3⋊Dic9) | 2 |
| C2×C4⋊(C3⋊Dic3) | 3 |
| C2×C4⋊Dic9 | 3 |