Finite Group DatabasebetaFinite Group DatabasebetaOrder 864.
258 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 258 conjugacy classes of subgroups — too many to draw. Only its 71 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. C2×C9×Dic6 | C2 | semidirect |
| 3. C2×C3×C9⋊C8 | C2 | semidirect |
| 4. #88426 | C2 | direct (N × H) |
| 13. C9×Dic6 | C22 | semidirect |
| 14. C3×C9⋊C8 | C22 | semidirect |
| 23. C2×C9⋊C8 | D3 | semidirect |
| 51. C9⋊C8 | C2×D3 | semidirect |
| 52. C2×C3×C9 | SD16 | semidirect |
| 59. C2×Dic6 | D9 | semidirect |
| 82. C3×C9 | C2×SD16 | semidirect |
| 100. Dic6 | C2×D9 | semidirect |
| 108. C2×C9 | #204 | semidirect |
| 135. C9 | C2×#204 | semidirect |
| 146. C2×C3 | #3675 | semidirect |
| 160. C3 | C2×#3675 | semidirect |
| 163. C2 | #88426 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4⋊(C3⋊D9) | 2 |
| C2×C9×Dic6 | 2 |
| C2×C3×C9⋊C8 | 2 |
| #88426 | 2 |
| C2×#3717 | 3 |
| C2×#3675 | 3 |