Finite Group DatabasebetaFinite Group DatabasebetaOrder 864.
336 conjugacy classes of subgroups; only the 140 normal subgroups are shown.
This group has 336 conjugacy classes of subgroups — too many to draw. Only its 140 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 |
|---|---|---|
| 2. C22×C3×Dic9 | C2 | semidirect |
| 3. C3×#3676 | C2 | semidirect |
| 4. C3×C4⋊Dic9 | C2 | semidirect |
| 5. C3×C4×Dic9 | C2 | semidirect |
| 7. D4×Dic9 | C3 | direct (N × H) |
| 9. C3×D4×C9 | C4 | semidirect |
| 22. C22×Dic9 | C2×C3 | semidirect |
| 23. #3676 | C2×C3 | semidirect |
| 24. C4⋊Dic9 | C2×C3 | semidirect |
| 25. C4×Dic9 | C2×C3 | semidirect |
| 28. C22×C3×C9 | C2×C4 | semidirect |
| 30. C3×C4×C9 | C2×C4 | semidirect |
| 33. C3×Dic9 | D4 | direct (N × H) |
| 46. D4×C9 | C3×C4 | semidirect |
| 82. C22×C9 | C2×C3×C4 | semidirect |
| 85. C4×C9 | C2×C3×C4 | semidirect |
| 88. Dic9 | C3×D4 | direct (N × H) |
| 90. C3×C9 | C4×D4 | semidirect |
| 95. C3×D4 | Dic9 | direct (N × H) |
| 133. C22×C3 | C2×Dic9 | semidirect |
| 141. C3×C4 | C2×Dic9 | semidirect |
| 148. C9 | C3×C4×D4 | semidirect |
| 150. D4 | C3×Dic9 | direct (N × H) |
| 170. C22 | C2×C3×Dic9 | semidirect |
| 175. C4 | C2×C3×Dic9 | semidirect |
| 177. C3 | D4×Dic9 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×D4×C9 | 2 |
| C22×C3×Dic9 | 2 |
| C3×#3676 | 2 |
| C3×C4⋊Dic9 | 2 |
| C3×C4×Dic9 | 2 |
| C3×D4×Dic3 | 3 |
| D4×Dic9 | 3 |