Finite Group DatabasebetaFinite Group DatabasebetaOrder 864.
336 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 336 conjugacy classes of subgroups — too many to draw. Only its 89 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⋊Dic9 | C2 | semidirect |
| 3. C2×Dic3×D9 | C2 | semidirect |
| 4. C9×#217 | C2 | semidirect |
| 5. (C2×D9)⋊Dic3 | C2 | semidirect |
| 6. Dic9⋊Dic3 | C2 | semidirect |
| 7. Dic3×Dic9 | C2 | semidirect |
| 15. C3×#611 | C4 | semidirect |
| 37. C22×C3×C9 | C2×C4 | semidirect |
| 41. C2×C3×D9 | C2×C4 | semidirect |
| 43. C3⋊Dic9 | D4 | semidirect |
| 46. C3×Dic9 | C2×C4 | semidirect |
| 64. #611 | Dic3 | semidirect |
| 87. #217 | D9 | semidirect |
| 111. C22×C9 | C2×Dic3 | semidirect |
| 115. C2×D9 | C2×Dic3 | semidirect |
| 122. Dic9 | C2×Dic3 | semidirect |
| 124. C3×C9 | C4×D4 | semidirect |
| 181. C22×C3 | C4×D9 | semidirect |
| 202. C9 | D4×Dic3 | semidirect |
| 232. C22 | Dic3×D9 | semidirect |
| 240. C3 | #611⋊C4 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C3⋊Dic9 | 2 |
| C2×C3×#611 | 2 |
| C2×Dic3×D9 | 2 |
| C9×#217 | 2 |
| (C2×D9)⋊Dic3 | 2 |
| Dic9⋊Dic3 | 2 |
| Dic3×Dic9 | 2 |
| #67⋊Dic3 | 3 |
| #611⋊C4 | 3 |